3 papers
math.AP2026
Geometry of the Atomic Condition
Jacek Jakimiuk, SÅawomir KolasiÅski, Maciej LeÅniak
The class AC of integrands satisfying the atomic condition was introduced by De Philippis, De Rosa, and Ghiraldin in 2018. These integrands give rise to Almgren elliptic geometric…
math.AP2026
Equivalence of Uniform Polyconvexity and Almgren Uniform Ellipticity for Lipschitz -Graph Test Pairs
Maciej Lesniak
We investigate the relationship between uniform polyconvexity of anisotropic geometric integrands and Almgren's uniform ellipticity. We first establish the converse implication for…
math.AP2025
On Polyconvexity and Almgren Uniform Ellipticity With Respect to Polyhedral Test Pairs
Maciej Lesniak
We study anisotropic geometric energy functionals defined on a class of k-dimensional surfaces in a Euclidean space. The classical notion of ellipticity, coming from Almgren, for s…