Connecting toric manifolds by conical Kahler-Einstein metrics

被引：7

作者：

Datar, Ved ^{[1
]}

Guo, Bin ^{[2
]}

Song, Jian ^{[3
]}

Wang, Xiaowei ^{[4
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[2] Columbia Univ, Dept Math, New York, NY 10027 USA

[3] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[4] Rutgers State Univ, Dept Math & Comp Sci, Newark, NJ 07102 USA

来源：

ADVANCES IN MATHEMATICS | 2018年 / 323卷

基金：

美国国家科学基金会;

关键词：

Conical Kahler-Einstein metrics; Toric manifolds; MONGE-AMPERE EQUATIONS; GREATEST LOWER BOUNDS; RICCI CURVATURE; SINGULARITIES; VARIETIES; FACTORIZATION; STABILITY; LIMITS;

D O I：

10.1016/j.aim.2017.10.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give criterions for the existence of toric conical Kahler-Einstein and Kahler-Ricci soliton metrics on any toric manifold in relation to the greatest Ricci and Bakry-Emery-Ricci lower bound. We also show that any two toric manifolds with the same dimension can be joined by a continuous path of toric manifolds with conical Kahler Einstein metrics in the Gromov-Hausdorff topology. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：38 / 83

页数：46

共 50 条

[21] Complete Kahler-Einstein manifolds
Kuehnel, Marco
COMPLEX AND DIFFERENTIAL GEOMETRY, 2011, 8 : 171 - 181
[22] Kahler-Einstein Metrics and Stability
Chen, Xiuxiong
Donaldson, Simon
Sun, Song
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014, 2014 (08) : 2119 - 2125
[23] Coupled Kahler-Einstein Metrics
Hultgren, Jakob
Nystrom, D. Witt
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2019, 2019 (21) : 6765 - 6796
[24] Existence of weak conical Kahler-Einstein metrics along smooth hypersurfaces
Yao, Chengjian
MATHEMATISCHE ANNALEN, 2015, 362 (3-4) : 1287 - 1304
[25] Einstein-Kahler metrics on symmetric toric Fano manifolds
Batyrev, VV
Selivanova, EN
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1999, 512 : 225 - 236
[26] REMARKS ON KAHLER-EINSTEIN MANIFOLDS
MATSUSHIMA, Y
NAGOYA MATHEMATICAL JOURNAL, 1972, 46 (MAR) : 161 - +
[27] SINGULAR KAHLER-EINSTEIN METRICS
Eyssidieux, Philippe
Guedj, Vincent
Zeriahi, Ahmed
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 22 (03) : 607 - 639
[28] Kahler-Einstein metrics on orbifolds and Einstein metrics on spheres
Ghigi, Alessandro
Kollar, Janos
COMMENTARII MATHEMATICI HELVETICI, 2007, 82 (04) : 877 - 902
[29] Quasi-potentials and Kahler-Einstein metrics on flag manifolds, II
Azad, H
Biswas, I
JOURNAL OF ALGEBRA, 2003, 269 (02) : 480 - 491
[30] Families of singular Kahler-Einstein metrics
Di Nezza, Eleonora
Guedj, Vincent
Guenancia, Henri
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2023, 25 (07) : 1249 - 2762

← 1 2 3 4 5 →