Inequalities for mixed p-affine surface area

Elisabeth Werner; Deping Ye

doi:10.1007/s00208-009-0453-2

Inequalities for mixed p-affine surface area

Elisabeth Werner, Deping Ye

Research output: Contribution to journal › Article › peer-review

58 Scopus citations

Abstract

We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed p-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of L_p affine surface areas, mixed p-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations.

Original language	English (US)
Pages (from-to)	703-737
Number of pages	35
Journal	Mathematische Annalen
Volume	347
Issue number	3
DOIs	https://doi.org/10.1007/s00208-009-0453-2
State	Published - 2010
Externally published	Yes

Bibliographical note

Funding Information:
E. Werner was partially supported by an NSF grant, a FRG-NSF grant and a BSF grant.

Keywords

52A20
53A15

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10.1007/s00208-009-0453-2

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abstract = "We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed p-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of Lp affine surface areas, mixed p-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations.",

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author = "Elisabeth Werner and Deping Ye",

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AU - Werner, Elisabeth

AU - Ye, Deping

N1 - Funding Information: E. Werner was partially supported by an NSF grant, a FRG-NSF grant and a BSF grant.

PY - 2010

Y1 - 2010

N2 - We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed p-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of Lp affine surface areas, mixed p-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations.

AB - We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed p-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of Lp affine surface areas, mixed p-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations.

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KW - 53A15

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EP - 737

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3

ER -

Inequalities for mixed p-affine surface area

Abstract

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