most citedSurfaces of constant principal-curvatures ratio in isotropic geometry

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math.DG2025

Families of surfaces with constant ratio of principal curvatures and Plateau's problem

Mikhail Skopenkov, Khusrav Yorov

This work is on surfaces with a constant ratio of principal curvatures. These CRPC surfaces generalize minimal surfaces but are much more challenging to construct. We propose a con…

math.DG2023★ 6 cited

Surfaces of constant principal-curvatures ratio in isotropic geometry

Khusrav Yorov, Mikhail Skopenkov, Helmut Pottmann

We study surfaces with a constant ratio of principal curvatures in Euclidean and simply isotropic geometries and characterize rotational, channel, ruled, helical, and translational…