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math.DG2026
Elastic Curves via Geometric Mechanics
Oliver Gross, Rohit Jammula, Albert Chern
Elastic curves are the mathematical shapes of thin elastic rods in equilibrium, with deep connections to mechanics, geometry, and computer graphics. Traditionally described as stat…
math.DG2025
Area formula for spherical polygons via prequantization
Albert Chern, Sadashige Ishida
We present a formula for the signed area of a spherical polygon via prequantization. In contrast to the traditional formula based on the Gauss-Bonnet theorem that requires measurin…
math.DG2024
Force-Free Fields are Conformally Geodesic
Albert Chern, Oliver Gross
In this paper, we establish an equivalence between force-free fields and conformally geodesic fields, and between harmonic fields and conformally eikonal fields in the context of c…