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UID:49c2d14aa26f178db23a7914a047b5aa
CATEGORIES:Special Colloquium
CREATED:20221214T151350
SUMMARY:A stability theory for isoperimetric and minimal area problems
LOCATION:Zoom
DESCRIPTION:Abstract: We offer a non-technical, panoramic view on some old and new resu
 lts concerning the quantitative description of minimizers and critical poin
 ts in basic geometric variational problems involving area. In the first par
 t of the talk we review basic results on almost-isoperimetric and almost-co
 nstant mean curvature boundaries, both in the Euclidean and in the Riemanni
 an setting. In the second part of the talk, we introduce the approximation 
 of possibly singular minimal surfaces by "soap films" with positive, small 
 volume. Finally, we revisit some of these results in the more physical cont
 ext of Allen-Cahn surface tension energies, and introduce a new convergence
  theorem for the diffused interface volume preserving mean curvature flow. 
 \n
X-ALT-DESC;FMTTYPE=text/html:<p style="background: white;">Abstract: We offer a non-technical, panoramic
  view on some old and new results concerning the quantitative description o
 f minimizers and critical points in basic geometric variational problems in
 volving area. In the first part of the talk we review basic results on almo
 st-isoperimetric and almost-constant mean curvature boundaries, both in the
  Euclidean and in the Riemannian setting. In the second part of the talk, w
 e introduce the approximation of possibly singular minimal surfaces by "soa
 p films" with positive, small volume. Finally, we revisit some of these res
 ults in the more physical context of Allen-Cahn surface tension energies, a
 nd introduce a new convergence theorem for the diffused interface volume pr
 eserving mean curvature flow.&nbsp;</p>
CONTACT:Francesco Maggi,  University of Texas at Austin
DTSTAMP:20260829T003007
DTSTART;TZID=America/New_York:20221215T140000
DTEND;TZID=America/New_York:20221215T150000
SEQUENCE:0
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