Smooth solutions to the \(L_p\) dual Minkowski problem (Q2419947)

The authors consider the $L_p$ dual Minkowski problem by using geometric variational methods. Under some technical restrictions, and using anisotropic Gauss-Kronecker curvature flows, they establish the existence of smooth solutions of the $L_p$ dual Minkowski problem when the given data is even; and seek conditions under which the only even, smooth, uniformly convex solution is the unit ball.