Curvature measures and soap bubbles beyond convexity
speaker: Mario Santilli (Università degli studi dell'Aquila)abstract: The celebrated uniqueness results of Alexandrov (1958) and Korevaar-Ros (1988) characterize the ball as the smooth bounded domain whose $ k $-th mean curvature is constant for some $ k = 1, ...., n $. A classical and important task in geometry is to provide extensions of these results in presence of singularities. Replacing the classical pointwise mean curvature functions by the curvature measures, Diskant (1968), for the gaussian curvature, and Schneider (1979) , for all curvature meaures, obtained these characterizations for arbitrary convex bodies. In this talk we present a result that extends the results of Diskant and Schneider beyond the convex regime, obtaining these characterizations for sets of positive reach. Joint work with Daniel Hug.
timetable:
Wed 14 Sep, 15:30 - 16:45, Aula Dini
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