Prescribing symmetric functions of the eigenvalues of the Ricci tensor

被引：60
作者：
Gursky, Matthew J. [1 ]
Viaclovsky, Jeff A. [2 ]
机构：
[1] Univ Notre Dame, Notre Dame, IN 46556 USA
[2] MIT, Cambridge, MA 02139 USA
来源：
ANNALS OF MATHEMATICS | 2007年 / 166卷 / 02期
关键词：
D O I：
10.4007/annals.2007.166.475
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric.
引用
收藏
页码：475 / 531
页数：57
相关论文
共 41 条
  • [1] Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds
    Azagra, D
    Ferrera, J
    López-Mesas, F
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 220 (02) : 304 - 361
  • [2] Bardi M, 1997, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Foundations and Applications, DOI [10.1007/978-0-8176-4755-1, DOI 10.1007/978-0-8176-4755-1]
  • [3] Besse A., 1987, Einstein manifolds, DOI 10.1007/978-3-540-74311-8
  • [4] Bishop R.L., 1964, GEOMETRY MANIFOLDS
  • [5] THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .3. FUNCTIONS OF THE EIGENVALUES OF THE HESSIAN
    CAFFARELLI, L
    NIRENBERG, L
    SPRUCK, J
    [J]. ACTA MATHEMATICA, 1985, 155 (3-4) : 261 - 301
  • [6] An a priori estimate for a fully nonlinear equation on four-manifolds
    Chang, SYA
    Gursky, MJ
    Yang, P
    [J]. JOURNAL D ANALYSE MATHEMATIQUE, 2002, 87 (1): : 151 - 186
  • [7] An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature
    Chang, SYA
    Gursky, MJ
    Yang, PC
    [J]. ANNALS OF MATHEMATICS, 2002, 155 (03) : 709 - 787
  • [8] Chavel I., 1993, Cambridge Tracts in Mathematics, V108
  • [9] CHEEGER J, 1982, J DIFFER GEOM, V17, P15
  • [10] Chen SYS, 2005, INT MATH RES NOTICES, V2005, P3403
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