4 papers
Classification of uniformly distributed measures of dimension in general codimension
Paul Laurain, Mircea Petrache
Starting with the work of Preiss on the geometry of measures, the classification of uniform measures in has remained open, except for and for compactly supporte…
Existence of Min-Max Free Boundary Disks Releasing the Width of a Manifold
Paul Laurain, Romain Petrides
We perform a replacement procedure in order to produce a free boundary minimal surface whose area achieves the min-max value over all disk sweepouts of a manifold whose boundary li…
Energy convexity of intrinsic bi-harmonic maps and applications I: spherical target
Paul Laurain, Longzhi Lin
Every harmonic map is an intrinsic bi-harmonic map as an absolute minimizer of the intrinsic bi-energy functional, therefore intrinsic bi-harmonic map and its heat flow are more ge…
Regularity and quantification for harmonic maps with free boundary
Paul Laurain, Romain Petrides
We prove a quantification result for harmonic maps with free boundary from arbitrary Riemannian surfaces into the unit ball of with bounded energy. This general…