An Aubin continuity path for shrinking gradient Kahler-Ricci solitons

被引：0

作者：

Cifarelli, Charles ^{[1
]}

Conlon, Ronan J. ^{[2
]}

Deruelle, Alix ^{[3
]}

机构：

[1] SUNT Stony Brook, Math Dept, Stony Brook, NY 11794 USA

[2] Univ Texas Dallas, Dept Math Sci, Richardson, TX 75080 USA

[3] Univ Paris Saclay, CNRS, Lab Math Orsay, F-91405 Orsay, France

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2024年 / 2024卷 / 815期

关键词：

MANIFOLDS; GEOMETRY; METRICS;

D O I：

10.1515/crelle-2024-0053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let D be a toric Kahler-Einstein Fano manifold. We show that any toric shrinking gradient Kahler-Ricci soliton on certain toric blowups of C x D satisfies a complex Monge-Ampere equation. We then set up an Aubin continuity path to solve this equation and show that it has a solution at the initial value of the path parameter. This we do by implementing another continuity method.

引用

页码：229 / 307

页数：79

共 50 条

[41] The moduli space of Fano manifolds with Kahler-Ricci solitons
Inoue, Eiji
ADVANCES IN MATHEMATICS, 2019, 357
[42] Fano Manifolds with Weak almost Kahler-Ricci Solitons
Wang, Feng
Zhu, Xiaohua
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (09) : 2437 - 2464
[43] BERGMAN KERNELS FOR A SEQUENCE OF ALMOST KAHLER-RICCI SOLITONS
Jiang, Wenshuai
Wang, Feng
Zhu, Xiaohua
ANNALES DE L INSTITUT FOURIER, 2017, 67 (03) : 1279 - 1320
[44] VARIATION OF COMPLEX STRUCTURES AND THE STABILITY OF KAHLER-RICCI SOLITONS
Hall, Stuart J.
Murphy, Thomas
PACIFIC JOURNAL OF MATHEMATICS, 2013, 265 (02) : 441 - 454
[45] COUPLED KAHLER-RICCI SOLITONS ON TORIC FANO MANIFOLDS
Hultgren, Jakob
ANALYSIS & PDE, 2019, 12 (08): : 2067 - 2094
[46] Classification of Generalized Kahler-Ricci Solitons on Complex Surfaces
Streets, Jeffrey
Ustinovskiy, Yury
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2021, 74 (09) : 1896 - 1914
[47] A new holomorphic invariant and uniqueness of Kahler-Ricci solitons
Tian, G
Zhu, XH
COMMENTARII MATHEMATICI HELVETICI, 2002, 77 (02) : 297 - 325
[48] Collapsing limits of the Kahler-Ricci flow and the continuity method
Zhang, Yashan
MATHEMATISCHE ANNALEN, 2019, 374 (1-2) : 331 - 360
[49] RIGIDITY OF GRADIENT SHRINKING RICCI SOLITONS
Yang, Fei
Zhang, Liangdi
ASIAN JOURNAL OF MATHEMATICS, 2020, 24 (04) : 533 - 547
[50] ON COMPLETE GRADIENT SHRINKING RICCI SOLITONS
Cao, Huai-Dong
Zhou, Detang
JOURNAL OF DIFFERENTIAL GEOMETRY, 2010, 85 (02) : 175 - 185

← 1 2 3 4 5 →