A Contribution of Liouville-Type Theorems to the Geometry in the Large of Hadamard Manifolds

被引：0

作者：

Mikes, Josef ^{[1
]}

Rovenski, Vladimir ^{[2
]}

Stepanov, Sergey ^{[3
]}

机构：

[1] Palacky Univ Olomouc, Dept Algebra & Geometry, Olomouc 77147, Czech Republic

[2] Univ Haifa, Dept Math, IL-3498838 Haifa, Israel

[3] Finance Univ, Dept Math, Moscow 125468, Russia

来源：

MATHEMATICS | 2022年 / 10卷 / 16期

关键词：

Hadamard manifold; subharmonic; harmonic and convex functions; isometric and harmonic diffeomorphisms; Killing and harmonic tensors; BOCHNER TECHNIQUE; HARMONIC-MAPPINGS;

D O I：

10.3390/math10162880

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A complete, simply connected Riemannian manifold of nonpositive sectional curvature is called a Hadamard manifold. In this article, we prove Liouville-type theorems for isometric and harmonic self-diffeomorphisms of Hadamard manifolds, as well as Liouville-type theorems for Killing-Yano, symmetric Killing and harmonic tensors on Hadamard manifolds.

引用

页数：14

共 50 条

[41] Some Liouville-type Theorems for the Stationary Ginsburg - Landau Equation on Quasi-model Riemannian Manifolds
Vikharev, S. S.
IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2015, 15 (02): : 127 - 135
[42] Liouville-type theorems for fractional Hardy–Hénon systems
Kui Li
Meng Yu
Zhitao Zhang
Nonlinear Differential Equations and Applications NoDEA, 2024, 31
[43] Gradient Estimates and Liouville-Type Theorems for a Nonlinear Elliptic Equation
Zhu Chaona
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2018, 31 (03): : 237 - 251
[44] Liouville-type theorems for the stationary inhomogeneous incompressible MHD equations
Liu, Pan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 521 (02)
[45] Liouville-type theorems for elliptic inequalities involving the Δλ-Laplace operator
Cung The Anh
Bui Kim My
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2016, 61 (07) : 1002 - 1013
[46] Hyperplane Separation Type Theorems in Hadamard Manifolds
Kroener, Axel
Kroener, Heiko
JOURNAL OF CONVEX ANALYSIS, 2022, 29 (02) : 519 - 529
[47] Liouville-type theorems for fractional Hardy-Henon systems
Li, Kui
Yu, Meng
Zhang, Zhitao
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 31 (01):
[48] Liouville-Type Theorems for the Stationary Ideal Magnetohydrodynamics Equations in Rn
Cai, Lv
Lai, Ning-An
Suen, Anthony
Yuen, Manwai
JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2024, 26 (04)
[49] Liouville-type theorems on the complete gradient shrinking Ricci solitons
Ge, Huabin
Zhang, Shijin
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2018, 56 : 42 - 53
[50] Liouville-type theorems for certain degenerate and singular parabolic equations
DiBenedetto, Emmanuele
Gianazza, Ugo
Vespri, Vincenzo
COMPTES RENDUS MATHEMATIQUE, 2010, 348 (15-16) : 873 - 877

← 1 2 3 4 5 →