141 citations · 441 across the 51 of their papers we have counts for
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Vectorial analogues of Cauchy's surface area formula
Daniel Hug, Rolf Schneider
Cauchy's surface area formula says that for a convex body in -dimensional Euclidean space the mean value of the -dimensional volumes of the orthogonal projections of…
Curvature measures and soap bubbles beyond convexity
Daniel Hug, Mario Santilli
Extending the celebrated results of Alexandrov (1958) and Korevaar-Ros (1988) for smooth sets, as well as the results of Schneider (1979) and the first author (1999) for arbitrary…
Reverse Alexandrov--Fenchel inequalities for zonoids
Károly J. Böröczky, Daniel Hug
The Alexandrov--Fenchel inequality bounds from below the square of the mixed volume of convex bodies in by the product o…
Extremizers and stability of the Betke--Weil inequality
Ferenc A. Bartha, Ferenc Bencs, Károly J. Böröczky +1
Let be a compact convex domain in the Euclidean plane. The mixed area of and can be bounded from above by , where is the perimete…
Strengthened inequalities for the mean width and the -norm
Károly J. Böröczky, Ferenc Fodor, Daniel Hug
Barthe proved that the regular simplex maximizes the mean width of convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball; o…
Integral geometry of pairs of hyperplanes or lines
Daniel Hug, Rolf Schneider
Crofton's formula of integral geometry evaluates the total motion invariant measure of the set of -dimensional planes having nonempty intersection with a given convex body. This…