20 citations · 147 across the 16 of their papers we have counts for
9 papers · 1 filter
Regularity for -systems of bounded distortion
Sławomir Kolasiński
We consider weak solutions of the -system , where $…
Rectifiability of every finite order for stationary integral varifolds
Sławomir Kolasiński
We give an alternative proof of a theorem of Brena, De Lellis and Franceschini (arXiv:2503.00649): the support of a stationary integral dimensional varifold in an open subset o…
Geometry of the Atomic Condition
Jacek Jakimiuk, Sławomir Kolasiński, Maciej Leśniak
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…
Perpendicularity and Locality for Codimension-One Varifolds with Bounded Anisotropic Mean Curvature
Sławomir Kolasiński, Mario Santilli
Suppose is an integrand associated with a uniformly convex -norm, and is a -dimensional varifold in an open subset of such…
Quadratic flatness and Regularity for Codimension-One Varifolds with Bounded Anisotropic Mean Curvature
Sławomir Kolasiński, Mario Santilli
We prove that if is a -dimensional varifold in an open subset of with bounded anisotropic mean curvature such that has locally…
Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets
Antonio De Rosa, Sławomir Kolasiński, Mario Santilli
Given an elliptic integrand of class , we prove that finite unions of disjoint open Wulff shapes with equal radii are the only volume-constrained critical points…
Equivalence of the ellipticity conditions for geometric variational problems
Antonio De Rosa, Sławomir Kolasiński
We exploit the so called atomic condition, recently defined by De Philippis, De Rosa, and Ghiraldin in [Comm. Pure Appl. Math.] and proved to be necessary and sufficient for the va…
Existence of solutions to a general geometric elliptic variational problem
Yangqin Fang, Sławomir Kolasiński
We consider the problem of minimising an inhomogeneous anisotropic elliptic functional in a class of closed dimensional subsets of which is stable under taking s…
Integral Menger curvature for sets of arbitrary dimension and codimension
Sławomir Kolasiński
We propose a notion of integral Menger curvature for compact, -dimensional sets in -dimensional Euclidean space and prove that finiteness of this quantity implies that the se…