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December 2020 Combinatorial Minimal Surfaces in Pseudomanifolds and Other Complexes
Weiyan HUANG, Daniel MEDICI, Nick MURPHY, Haoyu SONG, Scott A. TAYLOR, Muyuan ZHANG
Tokyo J. Math. 43(2): 497-527 (December 2020). DOI: 10.3836/tjm/1502179312

Abstract

We define combinatorial analogues of stable and unstable minimal surfaces in the setting of weighted pseudomanifolds and their generalizations. We prove that, under mild conditions, such combinatorial minimal surfaces always exist. We use a technique, adapted from work of Johnson and Thompson, called \emph{thin position}. Thin position is defined using orderings of the $n$-dimensional simplices of an $n$-dimensional pseudomanifold. In addition to defining and finding combinatorial minimal surfaces, from thin orderings, we derive invariants of even-dimensional closed simplicial pseudomanifolds called \emph{width} and \emph{trunk}. We study additivity properties of these invariants under connected sum and prove theorems analogous to those in knot theory and 3-manifold theory.

Citation

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Weiyan HUANG. Daniel MEDICI. Nick MURPHY. Haoyu SONG. Scott A. TAYLOR. Muyuan ZHANG. "Combinatorial Minimal Surfaces in Pseudomanifolds and Other Complexes." Tokyo J. Math. 43 (2) 497 - 527, December 2020. https://doi.org/10.3836/tjm/1502179312

Information

Published: December 2020
First available in Project Euclid: 20 July 2020

MathSciNet: MR4185846
Digital Object Identifier: 10.3836/tjm/1502179312

Subjects:
Primary: 57QO5
Secondary: 57M27

Rights: Copyright © 2020 Publication Committee for the Tokyo Journal of Mathematics

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Vol.43 • No. 2 • December 2020
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