Lie minimal Weingarten surfaces

2023/10/24 by Joseph Cho, Masaya Hara, Cho, Joseph +5
Physics and Astronomy · Mathematics · Biochemistry, Genetics and Molecular Biology · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Dermatological and Skeletal Disorders

paper · pdf · doi:10.48550/arxiv.2310.15695

Abstract

We consider Lie minimal surfaces, the critical points of the simplest Lie sphere invariant energy, in Riemannian space forms. These surfaces can be characterized via their Euler-Lagrange equations, which take the form of differential equations of the principal curvatures. Surfaces with constant mean curvature that satisfy these equations turn out to be rotational in their space form. We generalize in flat ambient space: here surfaces where the principal curvatures satisfy an affine relationship as well as elliptic linear Weingarten surfaces are rotational as well.

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