This article is available for purchase or by subscription. See below.
Abstract
|
Given a compact Riemannian manifold with boundary, we prove that the space of
embedded, which may be improper, free boundary minimal hypersurfaces with
uniform area and Morse index upper bound is compact in the sense of smoothly
graphical convergence away from finitely many points. We show that the limit of a
sequence of such hypersurfaces always inherits a nontrivial Jacobi field when it has
multiplicity one. In a forthcoming paper, we will construct Jacobi fields when the
convergence has higher multiplicity.
|
PDF Access Denied
We have not been able to recognize your IP address
3.141.244.201
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
free boundary minimal surfaces, compactness, Jacobi fields,
curvature estimates
|
Mathematical Subject Classification 2010
Primary: 53A10, 53C42
|
Milestones
Received: 29 May 2019
Revised: 10 October 2020
Accepted: 5 December 2020
Published: 26 January 2021
|
|