This article is available for purchase or by subscription. See below.
Abstract
|
We estimate the upper bound of volume of a closed positively or nonnegatively curved
Alexandrov space
with strictly convex boundary. We also discuss the equality case. In particular, the
boundary conjecture holds when the volume upper bound is achieved. Our theorem
can also be applied to Riemannian manifolds with nonsmooth boundary, which
generalizes Heintze and Karcher’s classical volume comparison theorem. Our main tool
is the gradient flow of semiconcave functions.
|
PDF Access Denied
We have not been able to recognize your IP address
3.138.200.66
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
Alexandrov space, volume comparison, convex boundary,
gradient flow
|
Mathematical Subject Classification
Primary: 53C23
|
Milestones
Received: 1 November 2020
Revised: 8 July 2021
Accepted: 14 August 2021
Published: 10 November 2021
|
|