Extremal Kahler-Einstein Metric for Two-Dimensional Convex Bodies

被引：2

作者：

Klartag, Bo'az ^{[1
,2
]}

Kolesnikov, Alexander V. ^{[3
]}

机构：

[1] Weizmann Inst Sci, Dept Math, IL-76100 Rehovot, Israel

[2] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

[3] Natl Res Univ Higher Sch Econ, Fac Math, Moscow 119048, Russia

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2019年 / 29卷 / 03期

基金：

美国国家科学基金会; 欧洲研究理事会;

关键词：

Monge-Ampere equation; Kahler-Einstein equation; Ricci tensors;

D O I：

10.1007/s12220-018-0077-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a convex body K Rn with the barycenter at the origin, we consider the corresponding Kahler-Einstein equation e-phi=detD2 phi. If K is a simplex, then the Ricci tensor of the Hessian metric D2 phi is constant and equals . We conjecture that the Ricci tensor of D2 phi for an arbitrary convex body KRn is uniformly bounded from above by and we verify this conjecture in the two-dimensional case. The general case remains open.

引用

页码：2347 / 2373

页数：27

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