Nonexistence of stable discrete maps into some homogeneous spaces of nonnegative curvature

Toru Kajigaya

doi:10.1007/s10231-023-01374-3

Nonexistence of stable discrete maps into some homogeneous spaces of nonnegative curvature

Toru Kajigaya

Department of Mathematics

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

Abstract

We consider stabilities for the weighted length or energy functional of a discrete map from a finite weighted graph (X,m_E) into a smooth Riemannian manifold (M, g). We prove the non-existence of a stable discrete minimal immersion or a non-constant stable discrete harmonic map from a finite weighted graph into certain homogeneous spaces, such as Kähler C-spaces of positive holomorphic sectional curvature and some simply-connected compact Riemannian symmetric spaces.

Original language	English
Pages (from-to)	563-603
Number of pages	41
Journal	Annali di Matematica Pura ed Applicata
Volume	203
Issue number	2
DOIs	https://doi.org/10.1007/s10231-023-01374-3
Publication status	Published - Apr 2024

Keywords

05C22
53C30
53C35
58E20
Compact symmetric spaces
Discrete harmonic maps
Discrete minimal immersions
Kähler C-spaces
Weighted graph

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abstract = "We consider stabilities for the weighted length or energy functional of a discrete map from a finite weighted graph (X,mE) into a smooth Riemannian manifold (M, g). We prove the non-existence of a stable discrete minimal immersion or a non-constant stable discrete harmonic map from a finite weighted graph into certain homogeneous spaces, such as K{\"a}hler C-spaces of positive holomorphic sectional curvature and some simply-connected compact Riemannian symmetric spaces.",

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KW - 53C30

KW - 53C35

KW - 58E20

KW - Compact symmetric spaces

KW - Discrete harmonic maps

KW - Discrete minimal immersions

KW - Kähler C-spaces

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ER -

Nonexistence of stable discrete maps into some homogeneous spaces of nonnegative curvature

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Keywords

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