A vertex-skipping property for almost-minimizers of the relative perimeter in convex sets
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- by Gian Paolo Leonardi and Giacomo Vianello;
- Trans. Amer. Math. Soc. 378 (2025), 3279-3295
- DOI: https://doi.org/10.1090/tran/9341
- Published electronically: March 5, 2025
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Abstract:
Given a convex domain $\Omega \subset \mathbb {R}^{3}$ and an almost-minimizer $E$ of the relative perimeter in $\Omega$, we prove that the closure of $\partial E \cap \Omega$ does not contain vertices of $\Omega$.References
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Bibliographic Information
- Gian Paolo Leonardi
- Affiliation: Dipartimento di Matematica, via Sommarive 14, IT-38123 Povo - Trento, Italy
- MR Author ID: 659964
- ORCID: 0000-0003-1944-312X
- Email: gianpaolo.leonardi@unitn.it
- Giacomo Vianello
- Affiliation: Dipartimento di Matematica, via Sommarive 14, IT-38123 Povo - Trento, Italy
- ORCID: 0000-0002-6664-6475
- Email: giacomo.vianello-1@unitn.it
- Received by editor(s): March 22, 2024
- Received by editor(s) in revised form: August 23, 2024
- Published electronically: March 5, 2025
- Additional Notes: The first author was partially supported by: PRIN 2017TEXA3H “Gradient flows, Optimal Transport and Metric Measure Structures”; PRIN 2022PJ9EFL “Geometric Measure Theory: Structure of Singular Measures, Regularity Theory and Applications in the Calculus of Variations” (financed by European Union - Next Generation EU, Mission 4, Component 2 - CUP:E53D23005860006); Grant PID2020-118180GB-I00 “Geometric Variational Problems”. The second author was supported by GNAMPA (INdAM) Project 2023: “Esistenza e proprietà fini di forme ottime”.
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 3279-3295
- MSC (2020): Primary 49Q05; Secondary 49Q10
- DOI: https://doi.org/10.1090/tran/9341