Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

1 Issue per year


CiteScore 2017: 0.65

SCImago Journal Rank (SJR) 2017: 1.063
Source Normalized Impact per Paper (SNIP) 2017: 0.833

Mathematical Citation Quotient (MCQ) 2017: 0.86

Open Access
Online
ISSN
2299-3274
See all formats and pricing
More options …

Isoperimetric Regions in Rn with Density rp

Wyatt Boyer / Bryan Brown / Gregory R. Chambers / Alyssa Loving / Sarah Tammen
Published Online: 2016-09-20 | DOI: https://doi.org/10.1515/agms-2016-0009

Abstract

We show that the unique isoperimetric regions in Rn with density rp for n ≥ 3 and p > 0 are balls with boundary through the origin.

Keywords: Isoperimetric; density

References

  • [1] Gregory R. Chambers, Isoperimetric regions in log-convex densities, J. Eur. Math. Soc., to appear. Google Scholar

  • [2] Jonathan Dahlberg, Alexander Dubbs, Edward Newkirk, Hung Tran, Isoperimetric regions in the plane with density rp, New York J. Math. 16 (2010), 31-51, http://nyjm.albany.edu/j/2010/16-4v.pdf. Google Scholar

  • [3] Alexander Díaz, Nate Harman, Sean Howe, David Thompson, Isoperimetric problems in sectors with density, Adv. Geom. 12 (2012), 589-619. Web of ScienceGoogle Scholar

  • [4] Max Engelstein, AnthonyMarcuccio, QuinnMaurmann, Taryn Pritchard, Isoperimetric problems on the sphere and on surfaces with density, New York J. Math. 15 (2009) 97-123, http://nyjm.albany.edu/j/2009/15-5.pdf. Google Scholar

  • [5] Frank Morgan, Regularity of isoperimetric hypersurfaces in Riemannian manifolds. (English summary) Trans. Amer. Math. Soc. 355 (2003), no. 12, 5041-5052 Google Scholar

  • [6] Frank Morgan, Manifolds with density, Notices Amer. Math. Soc. 52 (2005), 853-858, http://www.ams.org/notices/200508/ fea-morgan.pdf. Google Scholar

  • [7] Frank Morgan, Geometric Measure Theory, Academic Press, 4th ed., 2009, Chapters 18 and 15. Google Scholar

  • [8] Frank Morgan, Aldo Pratelli, Existence of isoperimetric regions inRn with density, Ann. Global Anal. Geom. 43 (2013), 331-365 Google Scholar

  • [9] Cesar Rosales, Antonio Cañete, Vincent Bayle, Frank Morgan, On the isoperimetric problem in Euclidean space with density. Calc. Var. PDE 31 (2008), 27-46. Google Scholar

About the article

Received: 2015-07-21

Accepted: 2016-08-07

Published Online: 2016-09-20


Citation Information: Analysis and Geometry in Metric Spaces, Volume 4, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2016-0009.

Export Citation

© 2016 W. Boyer et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Frank Morgan
The Mathematical Intelligencer, 2017, Volume 39, Number 4, Page 2

Comments (0)

Please log in or register to comment.
Log in