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math.DG2026
An Elementary Proof of Hopf's Curvatura Integra Theorem
Pavel Grinfeld
We provide an elementary proof of the key aspect of Hopf's curvatura integra theorem. Namely, we show that the total curvature, i.e. the surface integral of the Gauss-Kronecker cur…
math.DG2026
A Method for Preserving Geometric Meaning in the Calculus of Variations
Pavel Grinfeld
We discuss the advantages of the Calculus of Moving Surfaces over the Euler-Lagrange equation for optimization problems originating in Geometry. An extension of Tensor Calculus, it…