• Corpus ID: 227247544

# Compactness of the Space of Free Boundary CMC Surfaces with Bounded Topology

@article{Aiex2020CompactnessOT,
title={Compactness of the Space of Free Boundary CMC Surfaces with Bounded Topology},
author={Nicolau Sarquis Aiex and Hansol Hong},
journal={arXiv: Differential Geometry},
year={2020}
}
• Published 2 December 2020
• Mathematics
• arXiv: Differential Geometry
We prove that the space of free boundary CMC surfaces of bounded topology, bounded area and bounded boundary length is compact in the $C^k$ graphical sense away from a finite set of points. This is a CMC version of a result for minimal surfaces by Fraser-Li \cite{fraser.a-li.m2014}.

## References

SHOWING 1-10 OF 19 REFERENCES
Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary
• Mathematics
• 2012
We prove a lower bound for the first Steklov eigenvalue of embedded minimal hypersurfaces with free boundary in a compact $n$-dimensional manifold which has nonnegative Ricci curvature and strictly
Index estimates for surfaces with constant mean curvature in 3-dimensional manifolds
• Mathematics
Calculus of Variations and Partial Differential Equations
• 2020
We prove index estimates for closed and free boundary CMC surfaces in certain $3$-dimensional submanifolds of some Euclidean space. When the mean curvature is large enough we are able to prove that
• Mathematics
• 2017
We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong
Compactness of minimal hypersurfaces with bounded index
We prove a compactness result for minimal hypersurfaces with bounded index and volume, which can be thought of as an extension of the compactness theorem of Choi-Schoen (Invent. Math. 1985) to higher
Compactness of constant mean curvature surfaces in a three-manifold with positive Ricci curvature
In this paper we prove a compactness theorem for constant mean curvature surfaces with area and genus bound in three manifold with positive Ricci curvature. As an application, we give a lower bound
Rigidity of Free Boundary Surfaces in Compact 3-Manifolds with Strictly Convex Boundary
In this paper, we obtain an analogue of Toponogov theorem in dimension 3 for compact manifolds $$M^3$$M3 with nonnegative Ricci curvature and strictly convex boundary $$\partial M$$∂M. Here we obtain
Embedded minimal surfaces without area bounds in 3 - manifolds
• Engineering
• 1998
Two sheets are brought into accurately controlled registry with one another to form a laminate by indexing and retaining each sheet on a separate vacuum platen and then bringing the platens together
On the first variation of a varifold
Suppose M is a smooth m dimensional Riemannian manifold and k is a positive integer not exceeding m. Our purpose is to study the first variation of the k dimensional area integrand in M. Our main
A strict maximum principle for area minimizing hypersurfaces
It is a well-known consequence of the Hopf maximum principle that if Mv M2 are smooth connected minimal hypersurfaces which are properly embedded in an open subset U of an (n + l)-dimensional
Elliptic Partial Differential Equations of Second Order
• Mathematics
• 1997
We study in this chapter a class of partial differential equations that generalize and are to a large extent represented by Laplace’s equation. These are the elliptic partial differential equations