STRONG CONVEXITY FOR HARMONIC FUNCTIONS ON COMPACT SYMMETRIC SPACES

被引：0

作者：

Lippner, Gabor ^{[1
]}

Mangoubi, Dan ^{[2
]}

Mcguirk, Zachary ^{[2
]}

Yovel, Rachel ^{[2
]}

机构：

[1] Northeastern Univ, Dept Math, 360 Huntington Ave, Boston, MA 02115 USA

[2] Hebrew Univ Jerusalem, Einstein Inst Math, Edmond J Safra Campus, IL-91904 Jerusalem, Israel

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 04期

关键词：

Symmetric spaces; harmonic functions; Laplace powers; frequency; function; absolute monotonicity; convexity;

D O I：

10.1090/proc/15735

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let h be a harmonic function defined on a spherical disk. It is shown that Delta k|h|2 is nonnegative for all k is an element of N where Delta is the Laplace-Beltrami operator. This fact is generalized to harmonic functions defined on a disk in a normal homogeneous compact Riemannian manifold, and in particular in a symmetric space of the compact type. This complements a similar property for harmonic functions on Rn discovered by the first two authors and is related to strong convexity of the L2-growth function of harmonic functions.

引用

页码：1613 / 1622

页数：10

共 50 条

[31] Free, isometric circle actions on compact symmetric spaces
Eschenburg, JH
Kollross, A
Shankar, K
GEOMETRIAE DEDICATA, 2003, 102 (01) : 35 - 44
[32] ON HARMONIC STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC, CONJUGATE AND SYMMETRIC CONJUGATE POINTS
Liu, Zhi-Hong
Sun, Yong
Wang, Zhi-Gang
QUAESTIONES MATHEMATICAE, 2014, 37 (01) : 79 - 90
[33] On functions with given spherical means on symmetric spaces
Volchkov V.V.
Journal of Mathematical Sciences, 2011, 175 (4) : 402 - 412
[34] Convexity of energy functions of harmonic maps homotopic to covering maps of surfaces
Kim, Inkang
Wan, Xueyuan
Zhang, Genkai
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2024, 26 (10)
[35] Deriving harmonic functions in higher dimensional spaces
Qian, T
Sommen, F
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2003, 22 (02): : 275 - 288
[36] A symmetric convexity measure
Rosin, Paul L.
Mumford, Christine L.
COMPUTER VISION AND IMAGE UNDERSTANDING, 2006, 103 (02) : 101 - 111
[37] Applications of Symmetric Quantum Calculus to the Class of Harmonic Functions
Khan, Mohammad Faisal
Al-Shbeil, Isra
Aloraini, Najla
Khan, Nazar
Khan, Shahid
SYMMETRY-BASEL, 2022, 14 (10):
[38] Convexity of harmonic densities
Benko, David
Dragnev, Peter
Totik, Vilmos
REVISTA MATEMATICA IBEROAMERICANA, 2012, 28 (04) : 947 - 960
[39] Random Harmonic Functions in Growth Spaces and Bloch-type Spaces
Eikrem, Kjersti Solberg
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2014, 66 (02): : 284 - 302
[40] RIGIDITY OF RANK-ONE FACTORS OF COMPACT SYMMETRIC SPACES
Clarke, Andrew
ANNALES DE L INSTITUT FOURIER, 2011, 61 (02) : 491 - 509

← 1 2 3 4 5 →