Minkowski sums and symmetrizations

1988 ◽  
pp. 44-66 ◽  
Author(s):  
J. Bourgain ◽  
J. Lindenstrauss ◽  
V. D. Milman
Keyword(s):  
Minkowski Sums

scholarly journals Union of Hypercubes and 3D Minkowski Sums with Random Sizes

2021 ◽  
Author(s):  
Pankaj K. Agarwal ◽  
Haim Kaplan ◽  
Micha Sharir
Keyword(s):  
Minkowski Sums

Blob Metamorphosis based on Minkowski Sums

1996 ◽  
Vol 15 (3) ◽  
pp. 143-153 ◽  
Author(s):  
E. Galin ◽  
S. Akkouche
Keyword(s):  
Minkowski Sums

Continuous penetration depth computation for rigid models using dynamic Minkowski sums

2016 ◽  
Vol 78 ◽  
pp. 14-25 ◽  
Author(s):  
Youngeun Lee ◽  
Evan Behar ◽  
Jyh-Ming Lien ◽  
Young J. Kim
Keyword(s):  
Penetration Depth ◽  
Minkowski Sums

scholarly journals An elementary renewal theorem for random compact convex sets

1995 ◽  
Vol 27 (4) ◽  
pp. 931-942 ◽  
Author(s):  
Ilya S. Molchanov ◽  
Edward Omey ◽  
Eugene Kozarovitzky
Keyword(s):  
Support Function ◽  
Convex Sets ◽  
Compact Convex ◽  
Renewal Function ◽  
Renewal Theorem ◽  
Closed Sets ◽  
Random Closed Sets ◽  
Minkowski Sums ◽  
Image Position ◽  
Unit Vectors

A set-valued analog of the elementary renewal theorem for Minkowski sums of random closed sets is considered. The corresponding renewal function is defined as where are Minkowski (element-wise) sums of i.i.d. random compact convex sets. In this paper we determine the limit of H(tK)/t as t tends to infinity. For K containing the origin as an interior point, where hK(u) is the support function of K and is the set of all unit vectors u with EhA(u) > 0. Other set-valued generalizations of the renewal function are also suggested.

scholarly journals (Symplectic) leaves and (5d Higgs) branches in the Poly(go)nesian Tropical Rain Forest

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Marieke van Beest ◽  
Antoine Bourget ◽  
Julius Eckhard ◽  
Sakura Schäfer-Nameki
Keyword(s):  
Rain Forest ◽  
Tropical Rain Forest ◽  
Gauge Theories ◽  
Edge Coloring ◽  
Field Theories ◽  
Minkowski Sum ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Minkowski Sums ◽  
Symplectic Leaves

Abstract We derive the structure of the Higgs branch of 5d superconformal field theories or gauge theories from their realization as a generalized toric polygon (or dot diagram). This approach is motivated by a dual, tropical curve decomposition of the (p, q) 5-brane-web system. We define an edge coloring, which provides a decomposition of the generalized toric polygon into a refined Minkowski sum of sub-polygons, from which we compute the magnetic quiver. The Coulomb branch of the magnetic quiver is then conjecturally identified with the 5d Higgs branch. Furthermore, from partial resolutions, we identify the symplectic leaves of the Higgs branch and thereby the entire foliation structure. In the case of strictly toric polygons, this approach reduces to the description of deformations of the Calabi-Yau singularities in terms of Minkowski sums.

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