The world is rich in sensory information, and the challenge for any neural sensory system is to piece together the diverse messages from large arrays of feature detectors. In vision and auditory research, there has been speculation about the rules governing combination of signals from different neural channels: e.g. linear (city-block) addition, Euclidian (energy) summation, or a maximum rule. ...

Two new approaches are presented to establish the existence of polytopal solutions to the discrete-data Lp Minkowski problem for all p > 1. As observed by Schneider [21], the Brunn-Minkowski theory springs from joining the notion of ordinary volume in Euclidean d-space, R, with that of Minkowski combinations of convex bodies. One of the cornerstones of the Brunn-Minkowski theory is the classica...

We present a simple proof of Christer Borell’s general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell’s inequality to the log-Brunn-Minkowski inequality of Böröczky, Lutwak, Yang and Zhang.

We derive a Brunn-Minkowski-type inequality regarding the volume of the Minkowski sum of degenerate sets, namely, line sets. Let A 1 : : : A n be one dimensional sets of unit length, and v

We provide a curvature flow approach to the regular Christoffel-Minkowski problem. The speed of our is an entropy preserving type and contains global term.

Abstract We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if they exist, solve regular Orlicz–Minkowski problems. As an application, we obtain old new results even problems; corresponding $$L_p$$ L p </mm...

For some self-similar sets K ⇢ R we obtain certain lower bounds for the lower Minkowski dimension of K + E in terms of the lower Minkowski dimension of E.