General affine surface areas

Abstract

Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for $L_{\varphi }$ affine surface areas are established.

Next version; minor changes

References in corpus (1)

• General Lp affine isoperimetric inequalities

Cited by in corpus (21)

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• New Orlicz Affine Isoperimetric Inequalities
• Data depth and floating body
• Smoothness in the $l_p$ Minkowski problem for $p<1$
• On the monotone properties of general affine surface areas under the Steiner symmetrization
• A flow approach to the Musielak-Orlicz-Gauss image problem
• The Orlicz version of the $L_p$ Minkowski problem on $S^{n-1}$ for $-n<p<0$
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• Variational worn stones
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• Extremal general affine surface areas
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• Affine function valued valuations
• The Petty projection inequality for sets of finite perimeter
• Constrained convex bodies with extremal affine surface areas
• Affine Orlicz Pólya-Szegö principles and their equality cases
• The Minkowski problem in the Gaussian probability space
• A flow method for the dual Orlicz-Minkowski problem