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SUMMARY:Thomas Schmidt
DTSTART:20220201T170000Z
DTEND:20220201T180000Z
DTSTAMP:20260423T021017Z
UID:OSGA/89
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/89/">Pe
 rimeter functionals with measure datum</a>\nby Thomas Schmidt as part of O
 nline Seminar "Geometric Analysis"\n\n\nAbstract\nThe talk is concerned wi
 th perimeter functionals $\\mathscr{P}_\\mu$ given by\n\\[\n  \\mathscr{P}
 _\\mu[A]:=\\mathrm{P}(A)-\\mu(A^+)\n\\]\non sets $A\\subset{\\mathbb R}^n$
  of finite volume and finite perimeter\n$\\mathrm{P}(A)$\, where the fixed
  non-negative Radon measure $\\mu$ may be\nsingular and is (necessarily) e
 valuated on a suitable closure $A^+$ of\n$A$. It will be explained that se
 micontinuity and existence results for\n$\\mathscr{P}_\\mu$ crucially depe
 nd on a new type of isoperimetric condition\,\nwhich also admits some ($n{
 -}1$)-dimensional measures $\\mu$\, and exemplary\nconfigurations will be 
 discussed. The long-term goal of these considerations is\nto extend the va
 riational approach to prescribed mean curvature hypersurfaces in\nthe spir
 it of Caccioppoli\, De Giorgi\, Miranda\, Massari from $\\mathrm{L}^1$ mea
 n\ncurvature to mean curvature given by a possibly lower-dimensional measu
 re.\n
LOCATION:https://researchseminars.org/talk/OSGA/89/
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