We prove that the support of an $ m dimensional rectifiable varifold with a uniform lower bound on density and bounded generalized mean curvature can be covered \mathscr{H}^{m} almost everywhere by countable union $m$ submanifolds class \mathcal{C}^{2} $. obtain this result using notion arbitrary closed sets originally developed in stochastic geometry extending to our geometric setting techniqu...

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...

‎Abstract: In this paper, a new mixture modelling using the normal mean-variance mixture of Lindley (NMVL) distribution has been considered. The proposed model is heavy-tailed and multimodal and can be used in dealing with asymmetric data in various theoretic and applied problems. We present a feasible computationally analytical EM algorithm for computing the maximum likelihood estimates. T...