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math.DG2025
Area estimates for capillary cmc hypersurfaces with nonpositive Yamabe invariant
Leandro F. Pessoa, Erisvaldo Véras, Bruno Vieira
We prove area estimates for stable capillary (minimal) hypersurfaces with nonpositive Yamabe invariant that are properly immersed in a Riemannian -dimensional manifold…
math.DG2023
On splitting complete manifolds via infinity harmonic functions
Damião J. Araújo, Marco Magliaro, Luciano Mari +1
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-ne…
math.DG2018★ 29 cited
Maximum principles at infinity and the Ahlfors-Khas'minskii duality: an overview
Luciano Mari, Leandro Freitas Pessoa
This note is meant to introduce the reader to a duality principle for nonlinear equations that recently appeared in the literature. Motivations come from the desire to give a unify…