New Orlicz affine isoperimetric inequalities

By Deping Ye. 2014

56 citations recorded by the source corpus.

Abstract The Orlicz–Brunn–Minkowski theory received considerable attention recently, and many results in the L p -Brunn–Minkowski theory have been extended to their Orlicz counterparts. The aim of this paper is to develop Orlicz L ϕ affine and geominimal surface areas for a single convex body as well as for multiple convex bodies, which generalize the L p (mixed) affine and geominimal surface areas – fundamental concepts in the L p -Brunn–Minkowski theory. Our extensions are different from the general affine surface areas by Ludwig in [21] . Moreover, our definitions for Orlicz L ϕ affine and geominimal surface areas reveal that these affine invariants are essentially the infimum/supremum of V ϕ ( K , L ∘ ) , the Orlicz ϕ-mixed volume of K and the polar body of L, where L runs over all star bodies and all convex bodies, respectively, with volume of L equal to the volume of the unit Euclidean ball B 2 n . Properties for the Orlicz L ϕ affine and geominimal surface areas, such as affine invariance and monotonicity, are proved. Related Orlicz affine isoperimetric inequalities are also established.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/745e49f7355851354ae22c18ebcd8d095195e158

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In Applied Mathematics

1. Sudan Xing
2. Baocheng Zhu
3. Deping Ye

In Molecular Biology

1. Sudan Xing
2. Baocheng Zhu
3. Deping Ye

Citations in the corpus

• The Dual Orlicz–Minkowski Problem (2017, methodology): “In particular, the Orlicz mixed volumes of convex bodies have been obtained in [12, 46], which were used to discover, for instance, the Orlicz affine and geominimal surface areas and the Orlicz-John ellipsoid [47, 50, 57, 64].”