A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non-linear geometric features such as curved surface regions and feature lines. Our method uses a prescribed mean curvature flow (PMC) for simplicial surfaces which is based on three new contributions: 1. the definition and efficient calculation of a discrete shape operat...

We consider the Dirac operator D of a Lorentzian spin manifold of even dimension n 4. We prove, that the square D 2 of the Dirac operator on plane wave manifolds and the shifted operator D 2 ? K on Lorentzian space forms of constant sectional curvature K are of Huygens type. Furthermore, we study the Huygens property for coupled Dirac operators on 4-dimensional Lorentzian spin manifolds.

This article aims to investigate the curvature operator of second kind on Kähler manifolds. The first result states that an m-dimensional manifold with $$\frac{3}{2}(m^2-1)$$ -nonnegative (respectively, -nonpositive) must have constant nonnegative nonpositive) holomorphic sectional curvature. asserts a closed $$\left( \frac{3m^3-m+2}{2m}\right) $$ -positive has positive orthogonal bisectional c...

We show that an n-dimensional Riemannian manifold with n-nonnegative or n-nonpositive curvature operator of the second kind has restricted holonomy SO(n) is flat. The result does not depend on completeness and can be improved provided space Einstein Kähler. In particular, if a locally symmetric kind, then it constant curvature. When irreducible this to 3n2n+2n+4-nonnegative 3n2n+2n+4-nonpositiv...

One of the methods of building the fundamentals of Differential Geometry is the shape operator approach and everything you could want to know about a surface’s curvature is locked up in the shape operator. In this work we consider the variation of the shape operator and the normal, the mean and the principals curvatures and, at last, the Willmore energy, under infinitesimal bending of surface g...