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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…
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…
The Use of Geometric Quantities in the Tensor Description of a Euclidean Space
Pavel Grinfeld
We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors. We demonstrate the effectiveness of the approach by proving of a number of integra…
Accurate Computation of Laplace Eigenvalues by an Analytical Level Set Method
Pavel Grinfeld
This purpose of this write-up is to share an idea for accurate computation of Laplace eigenvalues on a broad class of smooth domains. We represent the eigenfunction as a linear…