Non-standard Constructions in Convex Geometry: Geometric Means of Convex Bodies

Vitali Milman; Liran Rotem; Eric Carlen; Mokshay Madiman; Elisabeth M. Werner

Non-standard Constructions in Convex Geometry: Geometric Means of Convex Bodies

Vitali Milman, Liran Rotem, Eric Carlen (Editor), Mokshay Madiman (Editor), Elisabeth M. Werner (Editor)

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to conference › Paper › peer-review

Abstract

In this note we discuss new constructions of convex bodies. By thinking of the polarity map K ↦ K∘ as the inversion x ↦ x−1 one may construct new bodies which were not previously considered in convex geometry. We illustrate this philosophy by describing a recent result of Molchanov, who constructed continued fractions of convex bodies.

Original language	American English
Pages	361-390
Number of pages	30
State	Published - 2017

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title = "Non-standard Constructions in Convex Geometry: Geometric Means of Convex Bodies",

abstract = "In this note we discuss new constructions of convex bodies. By thinking of the polarity map K ↦ K∘ as the inversion x ↦ x−1 one may construct new bodies which were not previously considered in convex geometry. We illustrate this philosophy by describing a recent result of Molchanov, who constructed continued fractions of convex bodies.",

author = "Vitali Milman and Liran Rotem and Eric Carlen and Mokshay Madiman and Werner, {Elisabeth M.}",

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language = "American English",

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AU - Rotem, Liran

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A2 - Madiman, Mokshay

A2 - Werner, Elisabeth M.

PY - 2017

Y1 - 2017

N2 - In this note we discuss new constructions of convex bodies. By thinking of the polarity map K ↦ K∘ as the inversion x ↦ x−1 one may construct new bodies which were not previously considered in convex geometry. We illustrate this philosophy by describing a recent result of Molchanov, who constructed continued fractions of convex bodies.

AB - In this note we discuss new constructions of convex bodies. By thinking of the polarity map K ↦ K∘ as the inversion x ↦ x−1 one may construct new bodies which were not previously considered in convex geometry. We illustrate this philosophy by describing a recent result of Molchanov, who constructed continued fractions of convex bodies.

M3 - Paper

SP - 361

EP - 390

ER -

Non-standard Constructions in Convex Geometry: Geometric Means of Convex Bodies

Abstract

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