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- W1580497895 abstract "The aim of this paper is to motivate the development of a Brunn-Minkowski theory for minimal surfaces. In 1988, H. Rosenberg and E. Toubiana studied a sum operation for finite total curvature complete minimal surfaces in $mathbb{R}^{3}$ and noticed that minimal hedgehogs of $mathbb{R}^{3} $ constitute a real vector space [14]. In 1996, the author noticed that the square root of the area of minimal hedgehogs of $mathbb{R}^{3}$ that are modelled on the closure of a connected open subset of $mathbb{S}^{2}$ is a convex function of the support function [5]. In this paper, the author (i) gives new geometric inequalities for minimal surfaces of $mathbb{R}^{3}$; (ii) studies the relation between support functions and Enneper-Weierstrass representations; (iii) introduces and studies a new type of addition for minimal surfaces; (iv) extends notions and techniques from the classical Brunn-Minkowski theory to minimal surfaces. Two characterizations of the catenoid among minimal hedgehogs are given." @default.
- W1580497895 created "2016-06-24" @default.
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- W1580497895 date "2004-04-01" @default.
- W1580497895 modified "2023-10-18" @default.
- W1580497895 title "A Brunn-Minkowski theory for minimal surfaces" @default.
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- W1580497895 doi "https://doi.org/10.1215/ijm/1258138401" @default.
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