Disks area-minimizing in mean convex Riemannian $n$-manifolds

Ezequiel Barbosa; Franciele Conrado

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arXiv · 2006.11788

Disks area-minimizing in mean convex Riemannian $n$-manifolds

Ezequiel Barbosa·Franciele Conrado

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Abstract

We prove the validity of an inequality involving a mean of the area and the length of the boundary of immersed disks whose boundaries are homotopically non-trivial curves in an oriented compact manifold which possesses convex mean curvature boundary, positive escalar curvature and admits a map to $\mathbb{D}^2\times T^{n}$ with nonzero degree, where $\mathbb{D}^2$ is a disk and $T^n$ is an $n$-dimensional torus. We also prove a rigidity result for the equality case when the boundary is totally geodesic. This can be viewed as a partial generalization of a result due to Lucas Ambr\'ozio in \cite{AMB} to higher dimensions.

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BibTeX RIS

Ezequiel Barbosa, Franciele Conrado. 2020-06-21. Disks area-minimizing in mean convex Riemannian $n$-manifolds. https://arxiv.org/abs/2006.11788

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