The L_p-Minkowski problem with super-critical exponents

2022/03/10 by Guang, Qiang, Li, Qi-Rui, Wang, Xu-Jia · 5 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.05099

Abstract

The L_p-Minkowski problem deals with the existence of closed convex hypersurfaces in ℝⁿ⁺¹ with prescribed p-area measures. It extends the classical Minkowski problem and embraces several important geometric and physical applications. The Existence of solutions has been obtained in the sub-critical case p>-n-1, but the problem remains widely open in the super-critical case p

Cited by

• The L_p chord Minkowski problem for super-critical exponent
• The capillary Orlicz-Minkowski problem
• Uniqueness of S₂-isotropic solutions to the isotropic L_p Minkowski problem
• Capillary L_p Minkowski Flows
• The L_p Dual Minkowski Problem for Group-Invariant Convex Bodies

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• The L_p chord Minkowski problem for super-critical exponent
• A non-existence result for the L_p-Minkowski problem
• Nonuniqueness and nonexistence results for the Lp-dual Minkowski problem with supercritical exponents
• The Weighted L^p Minkowski Problem