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PreprintCC BY 4.0arXiv

Continuity and monotonicity of weighted perimeters of convex bodies

  • Gyula Csató
  • Davide Giovagnoli
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Abstract

We investigate weighted perimeters of convex bodies in ℝn. Our main result states that the weighted perimeter is continuous with respect to the Hausdorff metric for every radial weight function. We also establish monotonicity under inclusion under suitable assumptions on the radial weight, and show that these assumptions are sharp. These results are applied to show the existence of minimizers for a shape optimization problem.

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Cite

BibTeXRIS
BibTeX
@misc{csato2026continuity,
  title = {{Continuity and monotonicity of weighted perimeters of convex bodies}},
  author = {Gyula Csató and Davide Giovagnoli},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11677},
  eprint = {2610.11677},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11677},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Continuity and monotonicity of weighted perimeters of convex bodies
AU  - Gyula Csató
AU  - Davide Giovagnoli
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11677
UR  - https://arxiv.org/abs/2610.11677
AB  - We investigate weighted perimeters of convex bodies in ℝ^n. Our main result states that the weighted perimeter is continuous with respect to the Hausdorff metric for every radial weight function. We also establish monotonicity under inclusion under suitable assumptions on the radial weight, and show that these assumptions are sharp. These results are applied to show the existence of minimizers for a shape optimization problem.
ER  -