A note on Chern-Yamabe problem

被引：6

作者：

Calamai, Simone ^{[1
]}

Zou, Fangyu ^{[2
]}

机构：

[1] Univ Firenze, Dipartimento Matemat & Informat Ulisse Dini, Via Morgagni 67-A, I-50134 Florence, Italy

[2] SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2020年 / 69卷

关键词：

Chern-Yamabe problem; Constant Chern scalar curvature;

D O I：

10.1016/j.difgeo.2020.101612

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded from below. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：14

共 50 条

[21] Hyperbolic Yamabe problem
KONG De-xing
LIU Qi
[J]. Applied Mathematics:A Journal of Chinese Universities, 2017, 32 (02) : 147 - 163
[22] THE EQUIVARIANT YAMABE PROBLEM
HEBEY, E
VAUGON, M
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 1993, 117 (02): : 241 - 286
[23] About the Lorentzian Yamabe problem
Nicolas Ginoux
[J]. Geometriae Dedicata, 2015, 174 : 287 - 309
[24] A COMPACTNESS THEOREM FOR THE YAMABE PROBLEM
Khuri, M. A.
Marques, F. C.
Schoen, R. M.
[J]. JOURNAL OF DIFFERENTIAL GEOMETRY, 2009, 81 (01) : 143 - 196
[25] Multiple solutions to the Yamabe problem
Yu. V. Egorov
Ya. Sh. Il’yasov
[J]. Doklady Mathematics, 2006, 74
[26] The Yamabe Problem for Distributional Curvature
Huaiyu Zhang
[J]. The Journal of Geometric Analysis, 2023, 33
[27] REGULARITY FOR THE SINGULAR YAMABE PROBLEM
MAZZEO, R
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1991, 40 (04) : 1277 - 1299
[28] Kodaira dimension and the Yamabe problem
LeBrun, C
[J]. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 1999, 7 (01) : 133 - 156
[29] On a fully nonlinear Yamabe problem
Ge, Yuxin
Wang, Guofang
[J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2006, 39 (04): : 569 - 598
[30] Yamabe Problem for Kropina Metrics
Behzad Najafi
Negin Youseflavi
Akbar Tayebi
[J]. Bulletin of the Iranian Mathematical Society, 2021, 47 : 323 - 333

← 1 2 3 4 5 →