Existence of CMC-foliations in asymptotically cuspidal manifolds
Claudio Arezzo, Karen Corrales
TL;DR
This paper proves the existence and uniqueness of constant mean curvature (CMC) foliations in asymptotically cuspidal manifolds and explores the isoperimetric problem without curvature restrictions across all dimensions.
Contribution
It establishes the existence and uniqueness of CMC foliations in a broad class of manifolds without curvature assumptions, extending previous results.
Findings
CMC foliation exists and is unique in asymptotically cuspidal manifolds
The results hold in any dimension without curvature restrictions
The paper analyzes the isoperimetric problem in this geometric setting
Abstract
In this paper we prove existence and uniqueness of a CMC foliation in asymptotically cuspidal manifolds. Moreover, we study the isoperimetric problem in this case. Our proof does not require any curvature assumption and it holds for any dimension.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology