TL;DR
This paper investigates the geometric profiles of inflated surfaces derived from convex polyhedra or flat surfaces with symmetry, characterizing them as solutions to a specific differential equation.
Contribution
It provides an explicit description of the profiles of inflated surfaces as solutions to a differential equation, expanding understanding of their geometric properties.
Findings
Profiles form a one-parameter family of curves
Profiles are solutions to a specific differential equation
Provides explicit characterization of inflated surface profiles
Abstract
We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show that such profiles are in a one-parameter family of curves which we describe explicitly as the solutions of a certain differential equation.
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