DIAMETER ESTIMATE FOR PLANAR L p DUAL MINKOWSKI PROBLEM

초록

In this paper, given a prescribed measure on S1 whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar Lp dual Minkowski problem when 0 < p < 1 and q ≥ 2. We also prove the uniqueness and positivity of solutions to the Lp Minkowski problem when the density of the measure is sufficiently close to a constant in Cα © 2024 American Mathematical Society.

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