Vol. 292, No. 2, 2018

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ISSN: 0030-8730
Locally helical surfaces have bounded twisting

David Bachman, Ryan Derby-Talbot and Eric Sedgwick

Vol. 292 (2018), No. 2, 257–272
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
Authors
David Bachman
Pitzer College
Claremont, CA
United States
Ryan Derby-Talbot
Quest University
Squamish, BC
Canada
Eric Sedgwick
DePaul University
Chicago, IL
United States