메뉴 건너뛰기




Volumn 11, Issue 3, 2001, Pages 589-608

Polar factorization of maps on Riemannian manifolds

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035618489     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001679     Document Type: Article
Times cited : (433)

References (33)
  • 2
    • 0032350790 scopus 로고    scopus 로고
    • On a reverse form of the Brascamp-Lieb inequality
    • F. BARTHE, On a reverse form of the Brascamp-Lieb inequality, Invent. Math. 134 (1998), 335-361.
    • (1998) Invent. Math. , vol.134 , pp. 335-361
    • Barthe, F.1
  • 3
    • 0032187452 scopus 로고    scopus 로고
    • Weak existence for the semi-geostrophic equations formulated as a coupled Monge-Ampère/transport problem
    • J.-D. BENAMOU, Y. BRENIER, Weak existence for the semi-geostrophic equations formulated as a coupled Monge-Ampère/transport problem, SIAM J. Appl. Math. 58 (1998), 1450-1461.
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1450-1461
    • Benamou, J.-D.1    Brenier, Y.2
  • 4
    • 0001016311 scopus 로고
    • Décomposition polaire et réarrangement monotone des champs de vecteurs
    • Y. BRENIER, Décomposition polaire et réarrangement monotone des champs de vecteurs, C.R. Acad. Sci. Paris Sér. I Math. 305 (1987), 805-808.
    • (1987) C.R. Acad. Sci. Paris Sér. I Math. , vol.305 , pp. 805-808
    • Brenier, Y.1
  • 5
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • Y. BRENIER, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math. 44 (1991), 375-417.
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 375-417
    • Brenier, Y.1
  • 6
    • 22044456113 scopus 로고    scopus 로고
    • Rearrangements and polar factorisation of countably degenerate functions
    • G.R. BURTON, R.J. DOUGLAS, Rearrangements and polar factorisation of countably degenerate functions, Proc. Roy. Soc. Edinburgh Sect. A, 128 (1998), 671-681.
    • (1998) Proc. Roy. Soc. Edinburgh Sect. A , vol.128 , pp. 671-681
    • Burton, G.R.1    Douglas, R.J.2
  • 7
    • 0031516222 scopus 로고    scopus 로고
    • Nondivergent elliptic equations on manifolds with nonnegative curvature
    • X. CABRÉ, Nondivergent elliptic equations on manifolds with nonnegative curvature, Comm. Pure Appl. Math. 50 (1997), 623-655.
    • (1997) Comm. Pure Appl. Math. , vol.50 , pp. 623-655
    • Cabré, X.1
  • 8
    • 85053493507 scopus 로고    scopus 로고
    • Allocation maps with general cost functions
    • "Partial Differential Equations and Applications," (P. Marcellini, et al., eds.), Dekker, New York
    • L. CAFFARELLI, Allocation maps with general cost functions, in "Partial Differential Equations and Applications," (P. Marcellini, et al., eds.), Lecture Notes in Pure and Appl. Math. 177 Dekker, New York (1996), 29-35.
    • (1996) Lecture Notes in Pure and Appl. Math. , vol.177 , pp. 29-35
    • Caffarelli, L.1
  • 9
    • 84968482174 scopus 로고
    • The regularity of mappings with a convex potential
    • L. A. CAFFARELLI, The regularity of mappings with a convex potential, J. Amer. Math. Soc. 5 (1992), 99-104.
    • (1992) J. Amer. Math. Soc. , vol.5 , pp. 99-104
    • Caffarelli, L.A.1
  • 10
    • 84990563964 scopus 로고
    • Boundary regularity of maps with convex potentials
    • L.A. CAFFARELLI, Boundary regularity of maps with convex potentials, Comm. Pure Appl. Math. 45 (1992), 1141-1151.
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 1141-1151
    • Caffarelli, L.A.1
  • 15
    • 0002425269 scopus 로고    scopus 로고
    • Applications of the Monge-Ampère equation and Monge transport problem to meteorology and oceanography
    • "Monge Ampère Equation: Applications to Geometry and Optimization" (L.A. Caffarelli, M. Milman, eds.), American Mathematical Society, Providence
    • M.J.P. CULLEN, R.J. DOUGLAS, Applications of the Monge - Ampère equation and Monge transport problem to meteorology and oceanography, in "Monge Ampère Equation: Applications to Geometry and Optimization" (L.A. Caffarelli, M. Milman, eds.), Contemp. Math. 226, American Mathematical Society, Providence (1998), 33-53.
    • (1998) Contemp. Math. , vol.226 , pp. 33-53
    • Cullen, M.J.P.1    Douglas, R.J.2
  • 17
    • 0039820628 scopus 로고
    • Length of curves on lip manifolds
    • Atti Accad. Naz. Lincei Cl. Sci. Fis. Math. Natur. Rend. (9)
    • G. DECECCO, G. PALMIERI, Length of curves on Lip manifolds, Atti Accad. Naz. Lincei Cl. Sci. Fis. Math. Natur. Rend. (9) Mat. Appl. 1 (1990), 215-221.
    • (1990) Mat. Appl. , vol.1 , pp. 215-221
    • DeCecco, G.1    Palmieri, G.2
  • 18
    • 0003073688 scopus 로고    scopus 로고
    • Partial differential equations and Monge-Kantorovich mass transfer
    • (R. Bott, et al., eds.), International Press, Cambridge
    • L.C. EVANS, Partial differential equations and Monge-Kantorovich mass transfer, in "Current Developments in Mathematics" (R. Bott, et al., eds.), International Press, Cambridge (1997), 26-78.
    • (1997) Current Developments in Mathematics , pp. 26-78
    • Evans, L.C.1
  • 19
    • 0003346795 scopus 로고
    • Measure theory and fine properties of functions
    • CRC Press, Boca Raton
    • L.C. EVANS, R.F. GARIEPY, Measure Theory and Fine Properties of Functions, Stud. Adv. Math. CRC Press, Boca Raton, 1992.
    • (1992) Stud. Adv. Math.
    • Evans, L.C.1    Gariepy, R.F.2
  • 20
    • 21844484336 scopus 로고
    • An elementary proof of the polar factorization of vector-valued functions
    • W. GANGBO, An elementary proof of the polar factorization of vector-valued functions, Arch. Rational Mech. Anal. 128 (1994), 381-399.
    • (1994) Arch. Rational Mech. Anal. , vol.128 , pp. 381-399
    • Gangbo, W.1
  • 22
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • W. GANGBO, R.J. MCCANN, The geometry of optimal transportation, Acta Math. 177 (1996), 113-161.
    • (1996) Acta Math. , vol.177 , pp. 113-161
    • Gangbo, W.1    McCann, R.J.2
  • 24
    • 0032343437 scopus 로고    scopus 로고
    • The variational formulation of the Fokker-Planck equation
    • R. JORDAN, D. KINDERLEHRER, F. OTTO, The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998), 1-17.
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1-17
    • Jordan, R.1    Kinderlehrer, D.2    Otto, F.3
  • 27
    • 84974004014 scopus 로고
    • Existence and uniqueness of monotone measure-preserving maps
    • R.J. MCCANN, Existence and uniqueness of monotone measure-preserving maps, Duke Math. J. 80 (1995), 309-323.
    • (1995) Duke Math. J. , vol.80 , pp. 309-323
    • McCann, R.J.1
  • 28
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • R.J. MCCANN, A convexity principle for interacting gases, Adv. Math. 128 (1997), 153-179.
    • (1997) Adv. Math. , vol.128 , pp. 153-179
    • McCann, R.J.1
  • 31
    • 0347420558 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • to appear
    • F. OTTO, The geometry of dissipative evolution equations: The porous medium equation, Comm. Partial Differential Equations, to appear.
    • Comm. Partial Differential Equations
    • Otto, F.1
  • 32
    • 0003696856 scopus 로고    scopus 로고
    • Mass transportation problems
    • Springer-Verlag, New York
    • S.T. RACHEV, L. RüSCHENDORF, Mass Transportation Problems, Probab. Appl. Springer-Verlag, New York, 1998.
    • (1998) Probab. Appl.
    • Rachev, S.T.1    Rüschendorf, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.