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Volumn 75, Issue 2, 2007, Pages 303-358

A matrix li-yau-hamilton estimate for kähler-ricci flow

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EID: 33847027231     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1175266268     Document Type: Article
Times cited : (49)

References (58)
  • 1
    • 51249170208 scopus 로고
    • Harnack inequalities for evolving hypersurfaces
    • B. Andrews, Harnack inequalities for evolving hypersurfaces, Math. Z. 217 (1994) 179-197.
    • (1994) Math. Z , vol.217 , pp. 179-197
    • Andrews, B.1
  • 2
    • 84972519663 scopus 로고
    • On classification of three-dimensional compact Kahler manifolds of nonnegative bisectional curvature
    • S. Bando, On classification of three-dimensional compact Kahler manifolds of nonnegative bisectional curvature, J. Differential Geom. 19 (1984) 283-297.
    • (1984) J. Differential Geom , vol.19 , pp. 283-297
    • Bando, S.1
  • 3
    • 0000820709 scopus 로고
    • On Harnack inequalities for the Kahler-Ricci flow
    • H.-D. Cao, On Harnack inequalities for the Kahler-Ricci flow, Invent. Math. 109 (1992) 247-263.
    • (1992) Invent. Math , vol.109 , pp. 247-263
    • Cao, H.-D.1
  • 4
    • 0031063197 scopus 로고    scopus 로고
    • Limits of solutions to the Kahler-Ricci flow
    • H.-D. Cao, Limits of solutions to the Kahler-Ricci flow, J. Differential Geom. 45 (1997) 257-272.
    • (1997) J. Differential Geom , vol.45 , pp. 257-272
    • Cao, H.-D.1
  • 5
    • 15244342270 scopus 로고    scopus 로고
    • Matrix Li-Yau-Hamilton estimates for heat equation on Kahler manifolds
    • H.-D. Cao & L. Ni, Matrix Li-Yau-Hamilton estimates for heat equation on Kahler manifolds, Math. Ann. 331 (2005) 795-807.
    • (2005) Math. Ann , vol.331 , pp. 795-807
    • Cao, H.-D.1    Ni, L.2
  • 6
    • 17044392689 scopus 로고    scopus 로고
    • A note on the uniformization of gradient Kahler-Ricci solitons
    • A. Chau & L.-F. Tam, A note on the uniformization of gradient Kahler-Ricci solitons, Math. Res. Lett. 12(1) (2005) 19-21.
    • (2005) Math. Res. Lett , vol.12 , Issue.1 , pp. 19-21
    • Chau, A.1    Tam, L.-F.2
  • 8
    • 0000596501 scopus 로고
    • On the upper estimate of the heat kernel of a complete Riemannian manifold
    • S.-Y. Cheng, P. Li, & S.-T. Yau, On the upper estimate of the heat kernel of a complete Riemannian manifold, Amer. J. Math. 103(5) (1981) 1021-1063.
    • (1981) Amer. J. Math , vol.103 , Issue.5 , pp. 1021-1063
    • Cheng, S.-Y.1    Li, P.2    Yau, S.-T.3
  • 9
    • 0000619988 scopus 로고
    • Heat equations on minimal submanifolds and their applications
    • S.-Y. Cheng, P. Li, & S.-T. Yau, Heat equations on minimal submanifolds and their applications, Amer. J. Math. 106(5) (1984) 1033-1065.
    • (1984) Amer. J. Math , vol.106 , Issue.5 , pp. 1033-1065
    • Cheng, S.-Y.1    Li, P.2    Yau, S.-T.3
  • 10
    • 84980136552 scopus 로고
    • A lower bound for the heat kernel
    • J. Cheeger & S.-T. Yau, A lower bound for the heat kernel, Comm. Pure Appl. Math. 34(4) (1981) 465-480.
    • (1981) Comm. Pure Appl. Math , vol.34 , Issue.4 , pp. 465-480
    • Cheeger, J.1    Yau, S.-T.2
  • 11
    • 0142259310 scopus 로고    scopus 로고
    • Interpolating between Li-Yau’s and Hamilton’s Harnack inequalities on a surface
    • B. Chow, Interpolating between Li-Yau’s and Hamilton’s Harnack inequalities on a surface, J. Partial Differential Equations 11(2) (1998) 137-140.
    • (1998) J. Partial Differential Equations , vol.11 , Issue.2 , pp. 137-140
    • Chow, B.1
  • 12
    • 21844501362 scopus 로고
    • A geometric interpretation of Hamilton’s Harnack inequality for the Ricci flow
    • B. Chow & S.-C. Chu, A geometric interpretation of Hamilton’s Harnack inequality for the Ricci flow, Math. Res. Lett. 2(6) (1995) 701-718.
    • (1995) Math. Res. Lett , vol.2 , Issue.6 , pp. 701-718
    • Chow, B.1    Chu, S.-C.2
  • 13
    • 0030305164 scopus 로고    scopus 로고
    • A geometric approach to the linear trace Harnack inequality for the Ricci flow
    • B. Chow & S.-C. Chu, A geometric approach to the linear trace Harnack inequality for the Ricci flow, Math. Res. Lett. 3(4) (1996) 549-568.
    • (1996) Math. Res. Lett , vol.3 , Issue.4 , pp. 549-568
    • Chow, B.1    Chu, S.-C.2
  • 15
    • 0039918029 scopus 로고    scopus 로고
    • Constrained and linear Harnack inqualities for parabolic equations
    • B. Chow & R. Hamilton, Constrained and linear Harnack inqualities for parabolic equations, Invent. Math. 129 (1997) 213-238.
    • (1997) Invent. Math , vol.129 , pp. 213-238
    • Chow, B.1    Hamilton, R.2
  • 16
    • 0142259311 scopus 로고    scopus 로고
    • New Li-Yau-Hamilton inequalities for the Ricci flow via the space-time approach
    • B. Chow & D. Knopf, New Li-Yau-Hamilton inequalities for the Ricci flow via the space-time approach, J. Differential Geom. 60(1) (2002) 1-54.
    • (2002) J. Differential Geom , vol.60 , Issue.1 , pp. 1-54
    • Chow, B.1    Knopf, D.2
  • 18
    • 0010800428 scopus 로고
    • A counterexample to the Transcendental Bezout problem
    • M. Cornalba & B. Shiffman, A counterexample to the ‘Transcendental Bezout problem', Ann. of Math. 96(2) (1972) 402-406.
    • (1972) Ann. Of Math. , vol.96 , Issue.2 , pp. 402-406
    • Cornalba, M.1    Shiffman, B.2
  • 19
    • 0035540757 scopus 로고    scopus 로고
    • A local monotonicity formula for mean curvature flow
    • K. Ecker, A local monotonicity formula for mean curvature flow, Ann. of Math. (2) 154(2) (2001) 503-525.
    • (2001) Ann. Of Math. (2) , vol.154 , Issue.2 , pp. 503-525
    • Ecker, K.1
  • 20
    • 13844253010 scopus 로고    scopus 로고
    • Progress in Nonlinear Differential Equations and their Applications, 57, Birkhuser Boston, Inc., Boston, MA
    • K. Ecker, Regularity Theory for Mean Curvature Flow, Progress in Nonlinear Differential Equations and their Applications, 57, Birkhuser Boston, Inc., Boston, MA, 2004.
    • (2004) Regularity Theory for Mean Curvature Flow
    • Ecker, K.1
  • 21
    • 13844271552 scopus 로고    scopus 로고
    • A survey of entropy methods for partial differential equations
    • L. Evans, A survey of entropy methods for partial differential equations, Bull. AMS. 41(4) (2004) 409-438.
    • (2004) Bull. AMS , vol.41 , Issue.4 , pp. 409-438
    • Evans, L.1
  • 23
    • 23744500873 scopus 로고    scopus 로고
    • Entropy and reduced distance for Ricci expanders
    • M. Feldman, T. Ilmanen, & L. Ni, Entropy and reduced distance for Ricci expanders, Jour. Geom. Anal. 15 (2005) 49-62.
    • (2005) Jour. Geom. Anal , vol.15 , pp. 49-62
    • Feldman, M.1    Ilmanen, T.2    Ni, L.3
  • 24
    • 0003257548 scopus 로고
    • Entire Holomorphic Mappings in One and Several Complex Variables
    • Princeton Press
    • P. Griffiths, Entire Holomorphic Mappings in One and Several Complex Variables, Annals of Mathematics Studies, 85, Princeton Press, 1976.
    • (1976) Annals of Mathematics Studies , vol.85
    • Griffiths, P.1
  • 25
    • 0000930976 scopus 로고
    • Nevanlinna theory and holomorphic mappings between algebraic varieties
    • P. Griffiths & J. King, Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta. Math. 130 (1973) 145 -220.
    • (1973) Acta. Math , vol.130
    • Griffiths, P.1    King, J.2
  • 27
    • 0141637246 scopus 로고    scopus 로고
    • The fundamental solution on manifolds with time-dependent metrics
    • C. Guenther, The fundamental solution on manifolds with time-dependent metrics, Jour. Geom. Anal. 12 (3) (2002) 425-436.
    • (2002) Jour. Geom. Anal , vol.12 , Issue.3 , pp. 425-436
    • Guenther, C.1
  • 28
    • 84972496750 scopus 로고
    • The Harnack estimate for the Ricci flow
    • R. Hamilton, The Harnack estimate for the Ricci flow, J. Differential Geom. 37(1) (1993) 225-243.
    • (1993) J. Differential Geom , vol.37 , Issue.1 , pp. 225-243
    • Hamilton, R.1
  • 29
    • 0001233266 scopus 로고
    • A matrix Harnack estimate for the heat equation
    • R. Hamilton, A matrix Harnack estimate for the heat equation, Comm. Anal. Geom. 1(1) (1993) 113-126.
    • (1993) Comm. Anal. Geom , vol.1 , Issue.1 , pp. 113-126
    • Hamilton, R.1
  • 30
    • 0000281411 scopus 로고
    • Monotonicity formulas for parabolic flows on manifolds
    • R. Hamilton, Monotonicity formulas for parabolic flows on manifolds, Comm. Anal. Geom. 1(1) (1993) 127-137.
    • (1993) Comm. Anal. Geom , vol.1 , Issue.1 , pp. 127-137
    • Hamilton, R.1
  • 32
    • 84972527004 scopus 로고
    • Asymptotic behavior for singularities of the mean curvature flow
    • G. Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geom. 31 (1990) 285-299.
    • (1990) J. Differential Geom , vol.31 , pp. 285-299
    • Huisken, G.1
  • 34
    • 0040460276 scopus 로고
    • Lp and mean value properties of subharmonic functions on Riemannian manifolds
    • p and mean value properties of subharmonic functions on Riemannian manifolds, Acta Math. 153 (1984) 279-301.
    • (1984) Acta Math , vol.153 , pp. 279-301
    • Li, P.1    Schoen, R.2
  • 35
    • 84968495783 scopus 로고
    • On the heat kernel of the Bergmann metric on algebraic varieties
    • P. Li & G. Tian, On the heat kernel of the Bergmann metric on algebraic varieties, J. Amer. Math. Soc. 8(4) (1995) 857-877.
    • (1995) J. Amer. Math. Soc , vol.8 , Issue.4 , pp. 857-877
    • Li, P.1    Tian, G.2
  • 37
    • 0000324115 scopus 로고
    • On the parabolic kernel of the Schrödinger operator
    • P. Li & S.-T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156(3-4) (1986) 153-201.
    • (1986) Acta Math , vol.156 , Issue.3-4 , pp. 153-201
    • Li, P.1    Yau, S.-T.2
  • 38
    • 0000478901 scopus 로고
    • An embedding theorem of complete Köahler manifolds of positive bisectional curvature onto affine algebraic varieties
    • N. Mok, An embedding theorem of complete Köahler manifolds of positive bisectional curvature onto affine algebraic varieties, Bull. Soc. Math. France 112(2) (1984) 197-250.
    • (1984) Bull. Soc. Math. France , vol.112 , Issue.2 , pp. 197-250
    • Mok, N.1
  • 39
    • 84972492734 scopus 로고
    • The uniformization theorem for compact Köhler manifolds of nonnegative holomorphic bisectional curvature
    • N. Mok, The uniformization theorem for compact Köhler manifolds of nonnegative holomorphic bisectional curvature, J. Differential Geom. 27 (1988) 179-214.
    • (1988) J. Differential Geom , vol.27 , pp. 179-214
    • Mok, N.1
  • 40
    • 84980078895 scopus 로고
    • A Harnack inequality for parabolic differential equations
    • J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964) 101-134.
    • (1964) Comm. Pure Appl. Math , vol.17 , pp. 101-134
    • Moser, J.1
  • 41
    • 0036056555 scopus 로고    scopus 로고
    • The Poisson equation and Hermitian-Einstein metrics on complete Kahler manifolds
    • L. Ni, The Poisson equation and Hermitian-Einstein metrics on complete Kahler manifolds, Indiana Univ. Math. J.51 (2002) 679-704.
    • (2002) Indiana Univ. Math. J , vol.51 , pp. 679-704
    • Ni, L.1
  • 42
    • 31544480995 scopus 로고    scopus 로고
    • Monotonicity and Köhler-Ricci flow
    • L. Ni, Monotonicity and Köhler-Ricci flow, Contemp. Math. 367 (2005) 149-165.
    • (2005) Contemp. Math , vol.367 , pp. 149-165
    • Ni, L.1
  • 43
    • 84867951130 scopus 로고    scopus 로고
    • The entropy formula for linear heat equation
    • addenda, Jour. Geom. Anal. 14 (2004) 329-334
    • L. Ni, The entropy formula for linear heat equation, Jour. Geom. Anal. 14 (2004), 85-98; addenda, Jour. Geom. Anal. 14 (2004) 329-334.
    • (2004) Jour. Geom. Anal , vol.14 , pp. 85-98
    • Ni, L.1
  • 44
    • 10044275047 scopus 로고    scopus 로고
    • A monotonicity formula on complete Kahler manifold with nonnegative bisectional curvature
    • L. Ni, A monotonicity formula on complete Kahler manifold with nonnegative bisectional curvature, J. Amer. Math. Soc. 17 (2004) 909-946.
    • (2004) J. Amer. Math. Soc , vol.17 , pp. 909-946
    • Ni, L.1
  • 45
    • 12344295405 scopus 로고    scopus 로고
    • Ricci flow and nonnegativity of sectional curvature
    • L. Ni, Ricci flow and nonnegativity of sectional curvature, Math. Res. Lett. 11 (2004) 883-904.
    • (2004) Math. Res. Lett , vol.11 , pp. 883-904
    • Ni, L.1
  • 46
    • 31544476876 scopus 로고    scopus 로고
    • Ancient solutions to Kahler-Ricci flow
    • L. Ni, Ancient solutions to Kahler-Ricci flow, Math. Res. Lett. 12 (2005) 633-654.
    • (2005) Math. Res. Lett , vol.12 , pp. 633-654
    • Ni, L.1
  • 47
    • 0038509978 scopus 로고    scopus 로고
    • Plurisubharmonic functions and the Kahler-Ricci flow
    • L. Ni & L.-F. Tam, Plurisubharmonic functions and the Kahler-Ricci flow, Amer. J. Math. 125 (2003), 623-654.
    • (2003) Amer. J. Math , vol.125 , pp. 623-654
    • Ni, L.1    Tam, L.-F.2
  • 48
    • 2642522292 scopus 로고    scopus 로고
    • Plurisubharmonic functions and the structure of complete Kahler manifolds with nonnegative curvature
    • L. Ni & L.-F. Tam, Plurisubharmonic functions and the structure of complete Kahler manifolds with nonnegative curvature, J. Differential Geom. 64 (2003) 457-524.
    • (2003) J. Differential Geom , vol.64 , pp. 457-524
    • Ni, L.1    Tam, L.-F.2
  • 49
    • 4043071271 scopus 로고    scopus 로고
    • Kahler-Ricci flow and the Poincare-Lelong equation
    • L. Ni & L.-F. Tam, Kahler-Ricci flow and the Poincare-Lelong equation, Comm. Anal. Geom. 12 (2004) 111-141.
    • (2004) Comm. Anal. Geom , vol.12 , pp. 111-141
    • Ni, L.1    Tam, L.-F.2
  • 51
    • 0008730823 scopus 로고
    • Uber Folgen und Scharen von analytischen und meromorphen Funktionen mehrerer Variabeln, sowie von analytischen Abbildungen
    • H. Rutishauser, Uber Folgen und Scharen von analytischen und meromorphen Funktionen mehrerer Variabeln, sowie von analytischen Abbildungen, Acta Math. 83 (1950) 249-325.
    • (1950) Acta Math , vol.83 , pp. 249-325
    • Rutishauser, H.1
  • 52
    • 84972510530 scopus 로고
    • Deforming the metric on complete Riemannian manifolds
    • W.X. Shi, Deforming the metric on complete Riemannian manifolds, J. Differential Geom. 30 (1989), 223-301.
    • (1989) J. Differential Geom , vol.30 , pp. 223-301
    • Shi, W.X.1
  • 53
    • 0030635298 scopus 로고    scopus 로고
    • Ricci flow and the uniformization on complete noncompact KUhler manifolds
    • W.X. Shi, Ricci flow and the uniformization on complete noncompact KUhler manifolds, J. Differential Geom. 45 (1997), 94-220.
    • (1997) J. Differential Geom , vol.45 , pp. 94-220
    • Shi, W.X.1
  • 54
    • 0040067146 scopus 로고
    • The growth of the area of a transcendental analytic set, I and II
    • W. Stoll, The growth of the area of a transcendental analytic set, I and II, Math. Ann. 156 (1964) 47-78, 144-170.
    • (1964) Math. Ann. 156 , vol.47 , Issue.78 , pp. 144-170
    • Stoll, W.1
  • 56
    • 0003278340 scopus 로고
    • The equidistribution Theory of Holomorphic Curves
    • Princeton University Press
    • H. Wu, The equidistribution Theory of Holomorphic Curves, Annals of Math. Studies, 64, Princeton University Press, 1970.
    • (1970) Annals of Math. Studies , vol.64
    • Wu, H.1
  • 57
    • 0000694048 scopus 로고
    • Polynomial functions on complete Kahler manifolds, Several complex variables and complex geometry
    • H. Wu, Polynomial functions on complete Kahler manifolds, Several complex variables and complex geometry, Proc. Symp. Pure Math. 52 (1989) 601-610.
    • (1989) Proc. Symp. Pure Math , vol.52 , pp. 601-610
    • Wu, H.1


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