Numerically Destabilizing Minimal Discs. Issue 3 (31st August 2022)

• Record Type: Journal Article
• Authors: Brubaker, Nicholas; Murphy, Thomas; Negron, K. Oskar
• Is Part Of: Experimental mathematics. Volume 31:Issue 3(2022)
• Page Start: 794
• Page End: 805
• Publication Date: 2022-08-31
• Subjects: Stability of minimal surfaces -- numerical spectral techniques -- bounded index; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2019.1692261
• Languages: English
• ISSNs: 1058-6458

Abstract

Abstract: When calculating the index of a minimal surface, the set of smooth functions on a domain with compact support is the standard setting to describe admissible variations. We show that the set of admissible variations can be widened in a geometrically meaningful manner leading to a more general notion of index. This allows us to produce explicit examples of destabilizing perturbations for the fundamental Scherk surface. For the dihedral Enneper surfaces we show that both the classical and modified index can be explicitly determined.