Minkowski addition and mixed volumes

1977 ◽  
Vol 6 (2) ◽  
Author(s):  
H. Groemer
2021 ◽  
Vol 388 ◽  
pp. 107887
Author(s):  
Francesco Della Pietra ◽  
Nunzia Gavitone ◽  
Chao Xia
Keyword(s):  

2001 ◽  
Vol 33 (1) ◽  
pp. 39-60 ◽  
Author(s):  
Wolfgang Weil

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.


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

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

2015 ◽  
Vol 17 (05) ◽  
pp. 1550003 ◽  
Author(s):  
Ilya Molchanov

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.


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

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