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Volumn 351, Issue 2, 1999, Pages 683-713

The heat Kernel weighted hodge laplacian on noncompact manifolds

Author keywords

Heat kernels; Hodge theory; Schr dinger operators; Weighted cohomology

Indexed keywords


EID: 22444452292     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02021-8     Document Type: Article
Times cited : (54)

References (38)
  • 1
    • 33646943615 scopus 로고
    • Anderson, L2 harmonie forms on complete Riemannian manifolds
    • Toshikazu Sunada, éd. Springer, Berlin MR 89j:58004
    • [A] Michael T. Anderson, L2 harmonie forms on complete Riemannian manifolds, in "Geometry and Analysis on Manifolds: Proceedings Katata-Kyoto 1987," (Toshikazu Sunada, éd.) Springer, Berlin (1988), 1-19. MR 89j:58004
    • (1988) In "Geometry and Analysis on Manifolds: Proceedings Katata-Kyoto 1987," , pp. 1-19
    • Michael, T.1
  • 3
    • 0002298999 scopus 로고
    • De Rham-Hodge-Kodaira decomposition in oo-dimensions
    • MR 92k:58007
    • [AM] A. Arai & I. Mitoma, De Rham-Hodge-Kodaira decomposition in oo-dimensions, Math. Ann. 291 (1991), 51-73. MR 92k:58007
    • (1991) Math. Ann. , vol.291 , pp. 51-73
    • Arai, A.1    Mitoma, I.2
  • 4
    • 84972541701 scopus 로고
    • The Witten complex and the degenerate Morse inequalities
    • MR 87m:58169
    • [Bi] Jean-Michel Bismut, The Witten complex and the degenerate Morse inequalities, J. Differential Geom. 23 (1986), 207-240. MR 87m:58169
    • (1986) J. Differential Geom. , vol.23 , pp. 207-240
    • Bismut, J.-M.1
  • 6
  • 7
    • 0001265427 scopus 로고
    • On the structure of complete manifolds of nonnegative curvature
    • MR 46:8121
    • [CG] J. Cheeger & D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. 96 (1972), 413443. MR 46:8121
    • (1972) Ann. of Math. , vol.96 , pp. 413-443
    • Cheeger, J.1    Gromoll, D.2
  • 8
    • 49549162581 scopus 로고
    • Essential self-adjointness of powers of generators of hyperbolic equations
    • MR 51:6119
    • [Che] Paul R. Chernoff, Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Anal. 12 (1973), 401-414. MR 51:6119
    • (1973) J. Funct. Anal. , vol.12 , pp. 401-414
    • Chernoff, P.R.1
  • 10
    • 0003939017 scopus 로고
    • Cambridge University Press, Cambridge, U. K., MR 90e:35123
    • [Dal] E. B. Davies, Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge, U. K., 1989. MR 90e:35123
    • (1989) Heat Kernels and Spectral Theory
    • Davies, E.B.1
  • 11
    • 0000343914 scopus 로고
    • Pointwise bounds on the space and time derivatives of heat kernels
    • MR 90k:58214
    • [Da2] B. B. Davies, Pointwise bounds on the space and time derivatives of heat kernels, 3. Operator Theory 21 (1989), 367-378. MR 90k:58214
    • (1989) Operator Theory 21 , pp. 367-378
    • Davies, B.B.1
  • 12
    • 84966200962 scopus 로고
    • L2-harmonic forms on rotationally symmetric Riemannian manifolds
    • MR 81e:58004
    • [Dod] Jozef Dodziuk, L2-harmonic forms on rotationally symmetric Riemannian manifolds, Proc. Amer. Math. Soc. 77 no. 3 (1979), 395-400. MR 81e:58004
    • (1979) Proc. Amer. Math. Soc. , vol.77 , Issue.3 , pp. 395-400
    • Dodziuk, J.1
  • 13
    • 34250250721 scopus 로고
    • The differential form spectrum of hyperbolic space
    • MR 82f:58085
    • [Don] Harold Donnelly, The differential form spectrum of hyperbolic space, Manuscripta Math. 33 (1981), 365-385. MR 82f:58085
    • (1981) Manuscripta Math. , vol.33 , pp. 365-385
    • Donnelly, H.1
  • 14
    • 0013479552 scopus 로고
    • Lower Bounds for the Eigenvalues of Riemannian Manifolds
    • MR 83g:58069
    • [DonL] Harold Donnelly & Peter Li, Lower Bounds for the Eigenvalues of Riemannian Manifolds, Michigan Math. J. 29 (1982), 149-161. MR 83g:58069
    • (1982) Michigan Math. J. , vol.29 , pp. 149-161
    • Donnelly, H.1    Li, P.2
  • 15
    • 0000532314 scopus 로고
    • On the differential form spectrum of negatively curved Riemannian manifolds
    • MR 851:58115
    • [DonX] Harold Donnelly & Prederico Xavier, On the differential form spectrum of negatively curved Riemannian manifolds, Amer. J. Math. 106 (1984), 169-185. MR 851:58115
    • (1984) Amer. J. Math. , vol.106 , pp. 169-185
    • Donnelly, H.1    Xavier, P.2
  • 17
    • 0030587376 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for pinned loop groups
    • MR 97h:58176
    • [DriL] Bruce Driver & Terry Lohrenz, Logarithmic Sobolev inequalities for pinned loop groups, J. Funct. Anal. 40 (1996), 381-448. MR 97h:58176
    • (1996) J. Funct. Anal. , vol.40 , pp. 381-448
    • Driver, B.1    Lohrenz, T.2
  • 18
    • 84972529251 scopus 로고
    • The Wüten Laplacian on negatively curved simply connected manifolds
    • MR 94j:58171
    • [ER] K. D. Ehvorthy & S. Rosenberg, The Wüten Laplacian on negatively curved simply connected manifolds, Tokyo J. Math. 16 (1992), 513-524. MR 94j:58171
    • (1992) Tokyo J. Math. , vol.16 , pp. 513-524
    • Ehvorthy, K.D.1    Rosenberg, S.2
  • 19
    • 84974002528 scopus 로고
    • The spectrum of the Laplacian of manifolds of positive curvature
    • MR 93d:58174
    • [EF1] Jose F. Escobar &: Alexandre Freire, The spectrum of the Laplacian of manifolds of positive curvature, Duke Math. J. 65, no. 1 (1992), 1-21. MR 93d:58174
    • (1992) Duke Math. J. , vol.65 , Issue.1 , pp. 1-21
    • Escobar, J.F.1    Freire, A.2
  • 20
    • 0002628313 scopus 로고
    • The differential form spectrum of manifolds of positive curvature
    • MR 94b:58097
    • [EF2] Jose F. Escobar & Alexandre Freire, The differential form spectrum of manifolds of positive curvature, Duke Math. J. 69, no. 1 (1993), 1-41. MR 94b:58097
    • (1993) Duke Math. J. , vol.69 , Issue.1 , pp. 1-41
    • Escobar, J.F.1    Freire, A.2
  • 21
    • 84952419852 scopus 로고
    • Hubert space methods in the theory of harmonic integrals
    • MR 16:957a
    • [Ga] Matthew P. Gaffney, Hubert space methods in the theory of harmonic integrals, Trans. Amer. Math. Soc. 78 (1955), 426-444. MR 16:957a
    • (1955) Trans. Amer. Math. Soc. , vol.78 , pp. 426-444
    • Gaffney, M.P.1
  • 22
    • 0001474422 scopus 로고
    • Function Theory on Manifolds which Possess a Pole
    • Springer, Berlin, MR 81a:53002
    • [GW] R. E. Greene & H. Wu, Function Theory on Manifolds Which Possess a Pole, Lecture Notes in Mathematics 699, Springer, Berlin, 1979. MR 81a:53002
    • (1979) Lecture Notes in Mathematics , vol.699
    • Greene, R.E.1    Wu, H.2
  • 23
    • 0013245677 scopus 로고
    • Heat kernel of a noncompact Riemannian manifold
    • Stochastic analysis (Ithaca, NY, 1993), MR 96f:58155
    • [Gri] A. A. Grigor'yan, Heat kernel of a noncompact Riemannian manifold, Stochastic analysis (Ithaca, NY, 1993), Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI 57 (1995), 239-263. MR 96f:58155
    • (1995) Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI , vol.57 , pp. 239-263
    • Grigor'Yan, A.A.1
  • 25
    • 0010999220 scopus 로고
    • Logarithmic Sobolev Inequalities on Path Space
    • MR 96e:58167
    • [Hs] Elton P. Hsu, Logarithmic Sobolev Inequalities on Path Space, C. R. Acad. Sei. Paris Sér. I Math. 320 (1995), 1009-1012. MR 96e:58167
    • (1995) C. R. Acad. Sei. Paris Sér. I Math. , vol.320 , pp. 1009-1012
    • Hsu, E.P.1
  • 26
    • 0001625316 scopus 로고
    • Analysis on Wiener spaces I. Nonlinear maps
    • MR 93a:58176
    • [K1] S. Kusuoka, Analysis on Wiener spaces I. Nonlinear maps, J. Funct. Anal. 98 (1991), 122-168. MR 93a:58176
    • (1991) J. Funct. Anal. , vol.98 , pp. 122-168
    • Kusuoka, S.1
  • 27
    • 0002445127 scopus 로고
    • Analysis on Wiener spaces II. Differential forms
    • MR 93c:58230
    • [K2] S. Kusuoka, Analysis on Wiener spaces II. Differential forms, J. Funct. Anal. 103 (1992), 229-274. MR 93c:58230
    • (1992) J. Funct. Anal. , vol.103 , pp. 229-274
    • Kusuoka, S.1
  • 28
    • 0004333703 scopus 로고
    • De Rham cohomology of Wiener-Riemannian manifolds
    • Kyoto, 1990," Math. Soc. Japan, Tokyo MR 93e:58198
    • [K3] S. Kusuoka, De Rham cohomology of Wiener-Riemannian manifolds, in "Proceedings of the International Congress of Mathematicians (Kyoto, 1990)," Math. Soc. Japan, Tokyo (1991), 1075-1082. MR 93e:58198
    • (1991) In "Proceedings of the International Congress of Mathematicians , pp. 1075-1082
    • Kusuoka, S.1
  • 29
    • 0000871992 scopus 로고    scopus 로고
    • The Zero-in-the-Spectrum Question
    • MR 97h:58145
    • John Lott, The Zero-in-the-Spectrum Question, Enseign. Math. (2) 42 (1996), 341-376. MR 97h:58145
    • (1996) Enseign. Math. (2) , vol.42 , pp. 341-376
    • Lott, J.1
  • 30
    • 0030267774 scopus 로고    scopus 로고
    • Short time behavior of the heat kernel and its logarithmic derivatives
    • MR 98c:58164
    • [MS] P. Malliavin & D. Stroock, Short time behavior of the heat kernel and its logarithmic derivatives, J. Differential Geomerty 44 (1996), 550-570. MR 98c:58164
    • (1996) J. Differential Geomerty , vol.44 , pp. 550-570
    • Malliavin, P.1    Stroock, D.2
  • 31
    • 33646944210 scopus 로고
    • The Exterior Algebra of Wiemann Manifolds
    • MR 58:2851
    • [P] M. Ann Piech, The Exterior Algebra of Wiemann Manifolds, J. Funct. Anal. 28 (1978), 279-308. MR 58:2851
    • (1978) J. Funct. Anal. , vol.28 , pp. 279-308
    • Ann Piech, M.1
  • 32
    • 0000119424 scopus 로고
    • R-Torsion and the Laplacian on Riemannian Manifolds
    • MR 45:4447
    • [RaS] D. B. Ray fe I. M. Singer, R-Torsion and the Laplacian on Riemannian Manifolds, Adv. Math. 7 (1971), 145-210. MR 45:4447
    • (1971) Adv. Math. , vol.7 , pp. 145-210
    • Rayfe, D.B.1    Singer, I.M.2
  • 34
  • 35
    • 0000448499 scopus 로고
    • De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space
    • MR 88h:58009
    • [Sh] Ichiro Shigekawa, De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space, J. Math. Kyoto Univ. 26 (1986), 191-202. MR 88h:58009
    • (1986) J. Math. Kyoto Univ. , vol.26 , pp. 191-202
    • Shigekawa, I.1
  • 36
    • 0000337964 scopus 로고    scopus 로고
    • An Estimate on the Hessian of the Heat Kernel
    • N. Ikeda et al. eds., Springer, Tokyo (1996). MR 97m:58212
    • [St] Daniel W. Stroock, An Estimate on the Hessian of the Heat Kernel, in "Itô's Stochastic Calculus and Probability Theory" (N. Ikeda et al. eds.), Springer, Tokyo (1996). MR 97m:58212
    • In "Itô's Stochastic Calculus and Probability Theory"
    • Stroock, D.W.1
  • 38
    • 84972500802 scopus 로고
    • Supersymmetry and Morse theory
    • MR 84b:58111
    • [Wi] Edward Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982), 661-692. MR 84b:58111
    • (1982) J. Differential Geom. , vol.17 , pp. 661-692
    • Witten, E.1


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