A Sharp Quantitative Alexandrov Inequality and Applications to Volume Preserving Geometric Flows in 3D
We study the asymptotic behavior of the volume preserving mean curvature and the Mullins-Sekerka flat flow in three dimensional space. Motivated by this, we establish a 3D sharp quantitative version of the Alexandrov inequality for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>C</mml:mi> <mml:mn>2</mml:mn></mml:msup> </mml:math> -regular sets with a perimeter bound.
Authors
- Massimiliano Morini (ORCID: https://orcid.org/0000-0001-7805-2212)
- Francesca Oronzio
- Vesa Julin (ORCID: https://orcid.org/0000-0002-1310-4904)
- Emanuele Spadaro (ORCID: https://orcid.org/0000-0003-2257-1958)
Institutions
- University of Parma (IT)
- JAMK University of Applied Sciences (FI)
- Sapienza University of Rome (IT)
- KTH Royal Institute of Technology (SE)
Publication Details
- Journal
- Archive for Rational Mechanics and Analysis
- Published
- 2025-11-21
- DOI
- https://doi.org/10.1007/s00205-025-02141-9
- Citations
- 1
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 3.73
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Kungliga Tekniska Högskolan
- Università degli Studi di Parma
- Jyväskylän Yliopisto
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni