skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Kakkar, Arjun"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; ; (, Missouri journal of mathematical sciences)
    The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-convex density conjecture, for many densities on Rn the answer is a sphere about the origin. We seek to generalize his results to some other spaces of revolution or to two di erent densities for volume and perimeter. We provide general results on existence and boundedness and a new approach to proving circles about the origin isoperimetric. 
    more » « less
    Accepted Manuscript Full Text Available
  2. ; ; ; ; ; ; ; ; (, Analysis and Geometry in Metric Spaces)
    Abstract The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝ N is the standard double bubble. We seek the optimal double bubble in ℝ N with density, which we assume to be strictly log-convex. For N = 1 we show that the solution is sometimes two contiguous intervals and sometimes three contiguous intervals. In higher dimensions we think that the solution is sometimes a standard double bubble and sometimes concentric spheres (e.g. for one volume small and the other large). 
    more » « less
    Full Text Available