On Splitting Complete Manifolds via Infinity Harmonic Functions-Reference-Cited by-同舟云学术

On Splitting Complete Manifolds via Infinity Harmonic Functions

Published:2024-08-14 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Araújo Damião J¹,Magliaro Marco²,Mari Luciano³,Pessoa Leandro F⁴

Affiliation:

1. Departamento de Matemática, Universidade Federal da Paraíba , 58059-900, João Pessoa - Paraíba ( Brazil )

2. Departamento de Matemática, Universidade Federal do Ceará , 60455-760, Fortaleza , ( Brazil )

3. Dipartimento di Matematica, Università degli studi di Milano , Via Saldini 50, 20133 Milano ( Italy )

4. Departamento de Matemática, Universidade Federal do Piauí , 64049-550, Teresina ( Brazil )

Abstract

Abstract In this paper, we prove some splitting results for manifolds supporting a non-constant infinity harmonic function which has at most linear growth on one side. Manifolds with non-negative Ricci or sectional curvature are considered. In dimension $2$, we extend Savin’s theorem on Lipschitz infinity harmonic functions in the plane to every surface with non-negative sectional curvature.

Funder

Conselho Nacional Desenvolvimento Cientifico e Tecnologico

Paraíba State Research Foundation

Abdus Salam International Centre for Theoretical Physics

Alexander von Humboldt Foundation

Progetti di Rilevante Interesse Nazionale

Publisher

Oxford University Press (OUP)

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnae176/58816615/rnae176.pdf

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