Smooth even strictly horospherically convex solutions exist for the horospherical p-Christoffel-Minkowski problem and the new p-shifted Weingarten problem in hyperbolic space for p≥−n, under convexity bounds on f.
B\"or\"oczky, The logarithmic Minkowski conjecture and the L_p -Minkowski problem, Adv
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The horospherical $p$-Christoffel-Minkowski and prescribed $p$-shifted Weingarten curvature problems in hyperbolic space
Smooth even strictly horospherically convex solutions exist for the horospherical p-Christoffel-Minkowski problem and the new p-shifted Weingarten problem in hyperbolic space for p≥−n, under convexity bounds on f.