John Gemmer, Brown University
Isometric Immersions and Pattern Formation in Thin Elastic Sheets
Swelling thin elastic sheets are archetypical examples of pattern forming systems which are often modeled as the minimum an elastic energy which is the sum of a strong stretching energy which penalizes deviations from a growth
induced geometry and a weak bending energy. A fundamental question is whether we can deduce the three dimensional configuration of the sheet given exact knowledge of the swelling pattern. Using a combination of analysis and numerical conjectures I will argue that the periodic patterns observed in nature correspond to low energy isometric immersions of an imposed geometry.