Critical loci of convex domains in the plane

Dmitry Kleinbock; Anurag Rao; Srinivasan Sathiamurthy

doi:10.1016/j.indag.2021.03.003

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Critical loci of convex domains in the plane

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Critical loci of convex domains in the plane

Dmitry Kleinbock, Anurag Rao and Srinivasan Sathiamurthy

Indagationes mathematicae, Vol.32(3), pp.719-728

05/01/2021

DOI: https://doi.org/10.1016/j.indag.2021.03.003

Abstract

Science & Technology

Mathematics

Physical Sciences

Let K be a bounded convex domain in R-2 symmetric about the origin. The critical locus of K is defined to be the (non-empty compact) set of lattices Lambda in R-2 of smallest possible covolume such that Lambda boolean AND K = {0}. These are classical objects in geometry of numbers; yet all previously known examples of critical loci were either finite sets or finite unions of closed curves. In this paper we give a new construction which, in particular, furnishes examples of domains having critical locus of arbitrary Hausdorff dimension between 0 and 1. (C) 2021 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

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Title: Critical loci of convex domains in the plane
Creators: Dmitry Kleinbock - Brandeis University, Department of Mathematics
Anurag Rao - Brandeis University, Department of Mathematics
Srinivasan Sathiamurthy - Carnegie Mellon Univ, Pittsburgh, PA 15213 USA
Publication Details: Indagationes mathematicae, Vol.32(3), pp.719-728
Publisher: Elsevier
Number of pages: 10
Grant note: DMS-1600814; DMS-1900560 / United States National Science Foundation, United States of America
Identifiers: 9924086667501921
Academic Unit: Department of Mathematics
Language: English
Resource Type: Journal article

Critical loci of convex domains in the plane

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