On integral boxes of minimal surface
Jonathan Rotg\'e, G\'erald Tenenbaum
TL;DR
This paper extends the study of minimal surface integral boxes from two dimensions to higher dimensions, providing estimates for edge lengths based on volume and minimal surface constraints.
Contribution
It introduces new estimates for the mean lengths of edges of integral boxes with minimal surface in higher dimensions, generalizing previous two-dimensional results.
Findings
Derived bounds for edge lengths based on volume and surface area
Extended minimal surface estimates to higher-dimensional boxes
Provided theoretical framework for minimal surface optimization
Abstract
Generalising the two-dimensional case, we provide estimates for the mean-values of the lengths of the edges of an integral box with given volume and minimal surface.
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Taxonomy
TopicsAnalytic and geometric function theory · Point processes and geometric inequalities · Geometric Analysis and Curvature Flows