English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Proof of the double bubble curvature conjecture

Daily, M. (2007). Proof of the double bubble curvature conjecture. Journal of Geometric Analysis, 17(1), 75-86.

Item is

Basic

show hide
Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-488C-4 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-488D-2
Genre: Journal Article

Files

show Files
hide Files
:
JoGA17-75.pdf (Publisher version), 532KB
Name:
JoGA17-75.pdf
Description:
-
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
eDoc_access: PUBLIC
License:
-

Locators

show

Creators

show
hide
 Creators:
Daily, Marilyn1, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

Content

show
hide
Free keywords: -
 Abstract: An area minimizing double bubble in $\mathbb R^n$ is given by two (not necessarily connected) regions which have two prescribed $n$-dimensional volumes whose combined boundary has least $(n\!-\!1)$-dimensional area. The double bubble theorem states that such an area minimizer is necessarily given by a standard double bubble, composed of three spherical caps. This has now been proven for $n=2,3,4$, but is, for general volumes, unknown for $ n\ge 5$. Here, for arbitrary $n$, we prove a conjectured lower bound on the mean curvature of a standard double bubble. This provides an alternative line of reasoning for part of the proof of the double bubble theorem in $\mathbb R^3$, as well as some new component bounds in $\mathbb R^n$.

Details

show
hide
Language(s): eng - English
 Dates: 2007
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: eDoc: 213914
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Journal of Geometric Analysis
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 17 (1) Sequence Number: - Start / End Page: 75 - 86 Identifier: -