Plank theorems and their applications: a survey
William Verreault
TL;DR
This survey explores plank problems in convex geometry, discussing their fundamental concepts and highlighting surprising applications of plank theorems across different mathematical fields.
Contribution
It provides a comprehensive overview of plank problems and reveals novel applications of plank theorems in various areas of mathematics.
Findings
Plank theorems have broad applications in convex geometry.
Surprising connections between plank problems and other mathematical fields.
The survey summarizes key open problems and recent advances.
Abstract
Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Optimization and Variational Analysis · Point processes and geometric inequalities