STRONG CONVEXITY FOR HARMONIC FUNCTIONS ON COMPACT SYMMETRIC SPACES

Gabor Lippner, Dan Mangoubi, Zachary McGuirk, Rachel Yovel

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)1613-1622
Number of pages10
JournalProceedings of the American Mathematical Society
Volume150
Issue number4
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022 American Mathematical Society

Keywords

  • Absolute monotonicity
  • Convexity
  • Frequency function
  • Harmonic functions
  • Laplace powers
  • Symmetric spaces

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