Skip navigation
Please use this identifier to cite or link to this item:
Title: The Alexandrov-Fenchel Inequality and its Extremal Structures
Authors: Shenfeld, Yair
Advisors: van Handel, Ramon
Contributors: Operations Research and Financial Engineering Department
Subjects: Mathematics
Issue Date: 2020
Publisher: Princeton, NJ : Princeton University
Abstract: The theory of convex bodies, developed by H. Minkowski (1903), began with the observation that the volume of a sum of convex bodies is a polynomial. The Alexandrov-Fenchel inequality (1937) established log-concavity relations between the coefficients of this polynomial. These relations have numerous applications extending beyond the theory of convex bodies itself. The characterization of the equality cases of this inequality has been unknown for more than 80 years. This thesis sheds new light on both the Alexandrov-Fenchel inequality itself and its equality cases. On the inequality side, we develop an analytic perspective on the Alexandrov-Fenchel inequality which leads to a new and simple proofs of it. On the equality side, we characterize the equality cases of the inequality for large classes of convex bodies, confirming conjectures of R. Schneider.
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Operations Research and Financial Engineering

Files in This Item:
File Description SizeFormat 
Shenfeld_princeton_0181D_13343.pdf597.95 kBAdobe PDFView/Download

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.