An intersection formula for Hausdorff rectifiable sets using mixed volumes of the associated zonoids

1992 ◽  
Vol 43 (1) ◽  
Author(s):  
Jan Rataj
Keyword(s):  
Mixed Volumes ◽  
Rectifiable Sets ◽  
Intersection Formula

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

scholarly journals Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets

2008 ◽  
Vol 360 (03) ◽  
pp. 1559-1581 ◽  
Author(s):  
S. V. Borodachov ◽  
D. P. Hardin ◽  
E. B. Saff
Keyword(s):  
Riesz Energy ◽  
Rectifiable Sets

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 FINE DELIGNE–LUSZTIG VARIETIES AND ARITHMETIC FUNDAMENTAL LEMMAS

2019 ◽  
Vol 7 ◽  
Author(s):  
XUHUA HE ◽  
CHAO LI ◽  
YIHANG ZHU
Keyword(s):  
Fixed Points ◽  
Character Formula ◽  
Shimura Varieties ◽  
Fundamental Lemma ◽  
Residual Characteristic ◽  
Intersection Formula

We prove a character formula for some closed fine Deligne–Lusztig varieties. We apply it to compute fixed points for fine Deligne–Lusztig varieties arising from the basic loci of Shimura varieties of Coxeter type. As an application, we prove an arithmetic intersection formula for certain diagonal cycles on unitary and GSpin Rapoport–Zink spaces arising from the arithmetic Gan–Gross–Prasad conjectures. In particular, we prove the arithmetic fundamental lemma in the minuscule case, without assumptions on the residual characteristic.

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