Minkowski addition and mixed volumes

1977 ◽  
Vol 6 (2) ◽  
Author(s):  
H. Groemer
Keyword(s):  
Mixed Volumes ◽  
Minkowski Addition

scholarly journals Symmetrization with respect to mixed volumes

2021 ◽  
Vol 388 ◽  
pp. 107887
Author(s):  
Francesco Della Pietra ◽  
Nunzia Gavitone ◽  
Chao Xia
Keyword(s):  
Mixed Volumes

Densities of mixed volumes for Boolean models

2001 ◽  
Vol 33 (1) ◽  
pp. 39-60 ◽  
Author(s):  
Wolfgang Weil
Keyword(s):  
Dimensional Space ◽  
Boolean Model ◽  
Boolean Models ◽  
Mixed Volumes ◽  
Explicit Formulae

In generalization of the well-known formulae for quermass densities of stationary and isotropic Boolean models, we prove corresponding results for densities of mixed volumes in the stationary situation and show how they can be used to determine the intensity of non-isotropic Boolean models Z in d-dimensional space for d = 2, 3, 4. We then consider non-stationary Boolean models and extend results of Fallert on quermass densities to densities of mixed volumes. In particular, we present explicit formulae for a planar inhomogeneous Boolean model with circular grains.

scholarly journals Gaussian Processes and Mixed Volumes

1987 ◽  
Vol 15 (1) ◽  
pp. 292-304 ◽  
Author(s):  
V. D. Milman ◽  
G. Pisier
Keyword(s):  
Gaussian Processes ◽  
Mixed Volumes

scholarly journals Dual mixed volumes and the slicing problem

2006 ◽  
Vol 207 (2) ◽  
pp. 566-598 ◽  
Author(s):  
Emanuel Milman
Keyword(s):  
Mixed Volumes ◽  
Dual Mixed Volumes

scholarly journals Continued fractions built from convex sets and convex functions

2015 ◽  
Vol 17 (05) ◽  
pp. 1550003 ◽  
Author(s):  
Ilya Molchanov
Keyword(s):  
Convex Functions ◽  
Continued Fractions ◽  
Convex Sets ◽  
Sufficient Conditions ◽  
Ordered Semigroup ◽  
Minkowski Addition ◽  
Partially Ordered ◽  
The Family ◽  
Sufficient Conditions For Convergence

In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalization of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Mixed Volumes

2019 ◽  
pp. 279-297
Author(s):  
Horst Martini ◽  
Luis Montejano ◽  
Déborah Oliveros
Keyword(s):  
Mixed Volumes
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