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SUMMARY:RIGIDITY AND STABILITY RESULTS FOR   THE GAUSS MEAN VALUE FORMULA
DTSTART:20180413T141500
DTSTAMP:20260527T190529Z
UID:4793bd45220f25bda8bdca1897152f666ae23b91fdd8648f001ffe8e
CATEGORIES:Conferences - Seminars
DESCRIPTION:Professeur Giovanni Cupini\, University de Bologne\nThe mean i
 ntegral of harmonic functions on balls equals the value of these\n\nfuncti
 ons at the center. This is the well known Gauss mean value theorem. In 197
 2\n\nKuran proved the reverse: if D is a bounded open set containing x\, s
 uch that the\n\nmean integral of harmonic functions on D equals the value 
 of these functions at x\,\n\nthen D is a ball centered at x. Two questions
  may be raised:\n\n(1) similar rigidity results can be proved for weighted
  mean integrals?\n\n(2) is the Gauss mean value formula stable? That is: i
 f the mean integral of\n\nharmonic functions on D centered at x is almost 
 equal to the value of these\n\nfunctions at x\, then D is almost a ball wi
 th center x?\n\nIn this talk I will discuss recent results on these issues
  obtained in collaboration\n\nwith E. Lanconelli (1) and with N. Fusco\, E
 . Lanconelli and X. Zhong (2\n\n)
LOCATION:MA A1 12 https://plan.epfl.ch/?room=MAA112
STATUS:CONFIRMED
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