STRONG CONVEXITY FOR HARMONIC FUNCTIONS ON COMPACT SYMMETRIC SPACES

Gabor Lippner; Dan Mangoubi; Zachary McGuirk; Rachel Yovel

doi:10.1090/proc/15735

STRONG CONVEXITY FOR HARMONIC FUNCTIONS ON COMPACT SYMMETRIC SPACES

Gabor Lippner, Dan Mangoubi, Zachary McGuirk, Rachel Yovel

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let h be a harmonic function defined on a spherical disk. It is shown that Δ^k|h|² is nonnegative for all k ∈ N where Δ 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.

Original language	English
Pages (from-to)	1613-1622
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	4
DOIs	https://doi.org/10.1090/proc/15735
State	Published - 2022

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Publisher Copyright:
© 2022 American Mathematical Society

Keywords

Absolute monotonicity
Convexity
Frequency function
Harmonic functions
Laplace powers
Symmetric spaces

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abstract = "Let h be a harmonic function defined on a spherical disk. It is shown that Δk|h|2 is nonnegative for all k ∈ N where Δ 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.",

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KW - Frequency function

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STRONG CONVEXITY FOR HARMONIC FUNCTIONS ON COMPACT SYMMETRIC SPACES

Abstract

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Keywords

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