Given a function f defined on the unit sphere, the L p Minkowski problem asks for a convex body K whose Lp surface area measure has density f with respect to the standard (n −1)-Hausdorff measure on the unit sphere. In this paper we deal with the generalization of this problem which arises in the Orlicz-Brunn-Minkowski theory when an Orlicz function substitutes the Lp norm and p is in the range (−n, 0). This problem is equivalent to solve a Monge-Ampere equation on the unit sphere, where the unknown is the support function of the convex body K.
The Orlicz version of the Lp Minkowski problem for −n < p < 0 / Bianchi G.; Boroczky K.J.; Colesanti A.. - In: ADVANCES IN APPLIED MATHEMATICS. - ISSN 0196-8858. - ELETTRONICO. - 111:(2019), pp. 0-0. [10.1016/j.aam.2019.101937]
The Orlicz version of the Lp Minkowski problem for −n < p < 0
Bianchi G.;Colesanti A.
2019
Abstract
Given a function f defined on the unit sphere, the L p Minkowski problem asks for a convex body K whose Lp surface area measure has density f with respect to the standard (n −1)-Hausdorff measure on the unit sphere. In this paper we deal with the generalization of this problem which arises in the Orlicz-Brunn-Minkowski theory when an Orlicz function substitutes the Lp norm and p is in the range (−n, 0). This problem is equivalent to solve a Monge-Ampere equation on the unit sphere, where the unknown is the support function of the convex body K.
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lp-negative-Orlicz-5b_revised_after_acceptance_AAM.pdf
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