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math.DG2023
Modulus of Concavity and Fundamental Gap Estimates on Surfaces
Gabriel Khan, Malik Tuerkoen, Guofang Wei
The fundamental gap of a domain is the difference between the first two eigenvalues of the Laplace operator. In a series of recent and celebrated works, it was shown that for conve…
math.DG2023
Curvature-Torsion Entropy for Twisted Curves under Curve Shortening Flow
Gabriel Khan
We study curve-shortening flow for twisted curves in (i.e., curves with nowhere vanishing curvature and torsion ) and define a notion of torsion-curvature ent…