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SUMMARY:Alberto Roncoroni
DTSTART:20210716T020000Z
DTEND:20210716T030000Z
DTSTAMP:20260418T132030Z
UID:2ndGAF/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/2ndGAF/1/">Q
 uantitative Studies of Alexadrov's Theorem</a>\nby Alberto Roncoroni as pa
 rt of The 2nd Geometric Analysis Festival\n\n\nAbstract\nAlexandrov's soap
  bubbles Theorem states that the spheres are the only closed\, connected\,
  and embedded hypersurfaces with constant mean curvature in the Euclidean 
 space.  The theorem holds true also in the so-called space forms and for m
 ore general functions of the principal curvatures. \n\nIn the talk we will
  present the classical result by Alexandrov together with two proofs: the 
 original one based on the\, nowadays called\, method of moving planes and 
 another one based on integral inequalities. Then we will show a quantitati
 ve stability result for hypersurfaces with almost constant mean curvature.
  In particular\, we will consider hypersurfaces\, satisfying the so-called
  uniform touching ball condition\, whose mean curvature is close to a cons
 tant and we will quantitatively describe\, in terms of the oscillation of 
 the mean curvature\, the closedness to a single ball.\n\nThis is based on 
 a joint work with G. Ciraolo and L. Vezzoni.\n
LOCATION:https://researchseminars.org/talk/2ndGAF/1/
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