Séminaire Analyse Harmonique
Quasiminimal sets and John domains in dimension 2 and 3
05
Nov. 2024
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Intervenant : Camille Labourie
Institution : Université de Lorraine
Heure : 10h45 - 11h30
Lieu : Bâtiment 307, salle 2L8

Quasiminimal sets are sets whose Hausdorff measure cannot be reduced beyond a certain percentage through deformation. This notion, introduced by David and Semmes, models soap films minimizing highly irregular energies, but also fracture without deformation in inhomogeneous solids. In this talk, I will present a joint work with Yana Teplitskaya to determine their optimal regularity in low dimension. This projet is motivated by the work of David and collaborators, who dealt with the case where a quasiminimal set only separates a finite number of components.

References:
L. and Teplitskaya, (preprint in preparation)
David et Semmes, Quasiminimal surfaces of codimension 1 and John domains
David et Pourmohammad, An optimal partition problem for the localization of eigenfunctions

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