An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature

被引：185

作者：

Chang, SYA ^{[1
]}

Gursky, MJ

Yang, PC

机构：

[1] Princeton Univ, Princeton, NJ 08544 USA

[2] Univ Notre Dame, Notre Dame, IN 46556 USA

来源：

ANNALS OF MATHEMATICS | 2002年 / 155卷 / 03期

关键词：

D O I：

10.2307/3062131

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigen-values of the Ricci tensor are positively pinched.

引用

页码：709 / 787

页数：79

共 38 条

[11] Chang SYA, 1999, AM J MATH, V121, P215
[12] CHANG SYA, 2002, IN PRESS J ANAL MATH, V87
[13] CHANG SYA, 1999, SPECTRAL PROBLEMS GE, V9, P28
[14] THE YAMABE FLOW ON LOCALLY CONFORMALLY FLAT MANIFOLDS WITH POSITIVE RICCI CURVATURE
CHOW, B
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (08) : 1003 - 1014
[15] DERDZINSKI A, 1983, COMPOS MATH, V49, P405
[16] DONALDSON SK, 1990, GEOMETRY MANIFOLDS
[17] EISENHART LP, 1966, RIEMANNIAN GEOMETRY
[18] EVANS LC, 1982, COMMUN PUR APPL MATH, V35, P333
[19] SHARP BORDERLINE SOBOLEV INEQUALITIES ON COMPACT RIEMANNIAN-MANIFOLDS
FONTANA, L
[J]. COMMENTARII MATHEMATICI HELVETICI, 1993, 68 (03) : 415 - 454
[20] THE TOPOLOGY OF 4-DIMENSIONAL MANIFOLDS
FREEDMAN, MH
[J]. JOURNAL OF DIFFERENTIAL GEOMETRY, 1982, 17 (03) : 357 - 453

← 1 2 3 4 →