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SUMMARY:Andrea Mondino (University of Oxford)
DTSTART:20211019T170000Z
DTEND:20211019T180000Z
DTSTAMP:20260423T035020Z
UID:OSGA/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/84/">Op
 timal Transport\, weak Laplacian bounds and minimal boundaries in non-smoo
 th spaces with Lower Ricci Curvature bounds</a>\nby Andrea Mondino (Univer
 sity of Oxford) as part of Online Seminar "Geometric Analysis"\n\n\nAbstra
 ct\nThe goal of the seminar is to report on recent joint work with\nDaniel
 e Semola\,  motivated by a question of Gromov to establish a “synthetic\
 nregularity theory" for minimal surfaces in non-smooth ambient spaces.\n\n
 In the setting of non-smooth spaces with lower Ricci Curvature bounds:\n<u
 l>\n<li>We establish a new principle relating lower Ricci Curvature bounds
  to the\npreservation of Laplacian bounds under the evolution via the Hopf
 -Lax\nsemigroup\;</li>\n<li>We develop an intrinsic viscosity theory of La
 placian bounds and prove\nequivalence with other weak notions of Laplacian
  bounds\;</li>\n<li>We prove sharp Laplacian bounds on the distance functi
 on from a set\n(locally) minimizing the perimeter: this corresponds to van
 ishing mean\ncurvature in the smooth setting\;</li>\n<li>We study the regu
 larity of boundaries of sets (locally) minimizing the\nperimeter\, obtaini
 ng sharp bounds on the Hausdorff co-dimension of the\nsingular set plus co
 ntent estimates and topological regularity of the\nregular set.</li>\n</ul
 >\nOptimal transport plays the role of underlying technical tool for addre
 ssing\nvarious points.\n
LOCATION:https://researchseminars.org/talk/OSGA/84/
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