Locally helical surfaces have bounded twisting

David Bachman, Ryan Derby-Talbot and Eric Sedgwick

Vol. 292 (2018), No. 2, 257–272

DOI: 10.2140/pjm.2018.292.257

Abstract

A topologically minimal surface may be isotoped into a normal form with respect to a fixed triangulation. If the intersection with each tetrahedron is simply connected, then the pieces of this normal form are triangles, quadrilaterals, and helicoids. Helical pieces can have any number of positive or negative twists. We show here that the net twisting of the helical pieces of any such surface in a given triangulated 3-manifold is bounded.

Keywords

normal surface, minimal surface, topologically minimal surface

Mathematical Subject Classification 2010

Primary: 57M99

Secondary: 53A10

Milestones

Received: 8 April 2016

Revised: 2 March 2017

Accepted: 2 June 2017

Published: 17 October 2017