We consider the graphical mean curvature flow of strictly area decreasing maps $f:M\to N$, where $M$ is a compact Riemannian manifold dimension $m>1$ and $N$ complete surface bounded geometry. prove long-time existence that property preserved, when bi-Ricci $BRic_M$ from below by sectional $\sigma_N$ $N$. In addition, we obtain smooth convergence to minimal map if $Ric_M\ge\sup\{0,{\sup}_N\sigm...

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...

We propose a new variational model for image denoising, which employs mean curvature information of the image surface (x, f(x)) induced by the given image f : Ω → R. Besides removing noise efficiently and preserving edges of objects, our method can also keep corners of objects as well as grey-scale intensity contrasts of images. We also compare our model with the classical ROF model [18].

We use the DPW construction [5] to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points with a common tangent plane. An appendix, by the t...