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Existence of solutions to the even dual Minkowski problem. (English) Zbl 1406.52017
The duals of Federer’s curvature measures within the dual Brunn-Minkowski theory have been recently described, and proved that the dual Minkowski problem has as special cases the Aleksandrov problem (when the index is 0) and the logarithmic Minkowski problem (when the index is the dimension of the ambient space). In this paper, existence of the solution to the even dual Minkowski problem is established under new sufficiency conditions than the ones previously used.

52A38 Length, area, volume and convex sets (aspects of convex geometry)
52A40 Inequalities and extremum problems involving convexity in convex geometry
35J96 Monge-Ampère equations
35J20 Variational methods for second-order elliptic equations
Full Text: DOI Euclid