Harmonic Mean Curvature Flow on Surfaces of Negative Gaussian Curvature

Gaussian and Mean Curvature of Subdivision Surfaces

By explicitly deriving the curvature of subdivision surfaces in the extraordinary points, we give an alternative, more direct account of the criteria necessary and sufficient for achieving curvature continuity than earlier approaches that locally parametrize the surface by eigenfunctions. The approach allows us to rederive and thus survey the important lower bound results on piecewise polynomia...

Timelike Surfaces with Harmonic Inverse Mean Curvature

In classical differential geometry, surfaces of constant mean curvature (CMC surfaces) have been studied extensively [1]. As a generalization of CMC surfaces, Bobenko [2] introduced the notion of surface with harmonic inverse mean curvature (HIMC surface). He showed that HIMC surfaces admit Lax representation with variable spectral parameter. In [5], Bobenko, Eitner and Kitaev showed that the G...

Mean Curvature Blowup in Mean Curvature Flow

In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.

Surfaces with Harmonic Inverse Mean Curvature and Painlev Equations

In this paper we study surfaces immersed in R such that the mean curvature function H satisfies the equation (1=H) = 0, where is the Laplace operator of the induced metric. We call them HIMC surfaces. All HIMC surfaces of revolution are classified in terms of the third Painlevé transcendent. In the general class of HIMC surfaces we distinguish a subclass of -isothermic surfaces, which is a gene...

Surfaces of Constant Mean Curvature