The Brunn–Minkowski inequality for volume differences

Leng, Gangsong

doi:10.1016/s0196-8858(03)00095-2

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Introduction and Statement Of Results3

V (K D) = V (K) − V (D)1

The Minkowski Inequality For Dual Quermassintegral Sum Of MI1

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Cited by 30 publications

(32 citation statements)

References 11 publications

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“…The following Brunn-Minkowski type inequality for volume difference functions was also established by Leng [6].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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On quotients of $i$th affine surface areas

Zhao¹

2013

Turk J Math

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“…The following Brunn-Minkowski type inequality for volume difference functions was also established by Leng [6].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…In fact, some more general versions on these types of inequalities were proved in [6] and [13], respectively.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

On quotients of $i$th affine surface areas

Zhao¹

2013

Turk J Math

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“…In 2004 Leng [11] defined the volume difference function of compact domains D and K, where D ⊆ K, by…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

“…The following Minkowski and Brunn-Minkowski type inequalities for volume difference functions were also established by Leng [11].…”

Section: V (K D) = V (K) − V (D)mentioning

confidence: 99%

On polars of Blaschke-Minkowski homomorphisms

Chang-jian¹

2012

MATH. SCAND.

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“…In [10], Leng introduce the concept of i-quermassintegral difference function of convex bodies as follows:…”

Section: The Minkowski Inequality For Dual Quermassintegral Sum Of MImentioning

confidence: 99%

Inequalities for dual quermassintegrals of mixed intersection bodies

Zhao

Leng

2005

Proc. Math. Sci.

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Abstract. In this paper, we first introduce a new concept of dual quermassintegral sum function of two star bodies and establish Minkowski's type inequality for dual quermassintegral sum of mixed intersection bodies, which is a general form of the Minkowski inequality for mixed intersection bodies. Then, we give the AleksandrovFenchel inequality and the Brunn-Minkowski inequality for mixed intersection bodies and some related results. Our results present, for intersection bodies, all dual inequalities for Lutwak's mixed prosection bodies inequalities.

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The Brunn–Minkowski inequality for volume differences

Cited by 30 publications

References 11 publications

On quotients of $i$th affine surface areas

On quotients of $i$th affine surface areas

On polars of Blaschke-Minkowski homomorphisms

Inequalities for dual quermassintegrals of mixed intersection bodies

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