Skip to Main content Skip to Navigation
Reports

On convex sets that minimize the average distance.

Abstract : Abstract: In this paper we study the compact and convex sets K in the plane, that minimize the average of dist(x,K) with respect to x, and according to a given probability measure, and with volume or perimeter constraints on the set K. We compute in particular the second order derivative of the functional and use it to exclude smooth points of positive curvature for the problem with volume constraint. The problem with perimeter constraint behaves differently since polygons are never minimizers. Finally using a purely geometrical argument from Tilli we can prove that any arbitrary convex set can be a minimizer when both perimeter and volume constraints are considered.
Document type :
Reports
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-00564109
Contributor : Christian David <>
Submitted on : Wednesday, February 9, 2011 - 10:17:21 AM
Last modification on : Monday, January 18, 2021 - 9:18:02 PM
Long-term archiving on: : Saturday, December 3, 2016 - 4:35:22 AM

File

R11009.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00564109, version 1

Citation

Antoine Lemenant, Edoardo Mainini. On convex sets that minimize the average distance.. 2011. ⟨hal-00564109⟩

Share

Metrics

Record views

255

Files downloads

328