Related papers: A sharp inscribed radius estimate for fully nonlin…

We consider inviscid flow with isentropic coefficient greater than one. For flow along smooth infinite protruding corners we attempt to impose a nonzero limit for velocity at infinity at the upstream wall. We prove that the problem does not…

This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and…

Oriented circular cylinders in an opaque medium are used to represent certain microstructural objects in steel. The opaque medium is sliced parallel to the cylinder axes of symmetry and the cut-plane contains the observable rectangular…

In this paper, we investigate the prescribed total geodesic curvature problem for generalized circle packing metrics in hyperbolic background geometry on surfaces with infinite cellular decompositions. To address this problem, we introduce…

We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability conditions. We study the flow with Sinus profile in details…

We study fully nonlinear elliptic equations on Hermitian manifolds through blow-up argument and partial uniform ellipticity. We apply our results to draw geometric conclusions on finding conformal Hermitian metrics with prescribed…

Over a bounded strictly convex domain in $\mathbb{R}^n$ with smooth boundary, we establish a priori gradient estimate for an anisotropic mean curvature flow with prescribed contact angle and Neumann boundary conditions. The estimates…

In this paper we present several curvature estimates for solutions of the Ricci flow which depend on smallness of certain local integrals of the norm of the Riemann curvature tensor.

In this work, we prove uniqueness for complete non-compact Ricci flow with scaling invariant curvature bound. This generalizes the earlier work of Chen-Zhu, Kotschwar and covers most of the example of Ricci flows with unbounded curvature.…

In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to…

We obtain sharp bounds for the number of n-cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. En route, we prove some sharp estimates on power…

We present the results of a large-scale simulation of a Dynamically Triangulated Random Surface with extrinsic curvature embedded in three-dimensional flat space. We measure a variety of local observables and use a finite size scaling…

The classical problem of the flow over a circular cylinder at Reynolds number 40 is considered using an accurate pseudo-spectral code. A new set of boundary conditions is proposed to improve the representation of the infinite flow domain,…

We study the stability of two-dimensional inviscid flows in an annulus between two porous cylinders with respect to three-dimensional perturbations. The basic flow is irrotational, and both radial and azimuthal components of the velocity…

We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.

This paper studies normalized Ricci flow on a nonparabolic surface, whose scalar curvature is asymptotically -1 in an integral sense. By a method initiated by R. Hamilton, the flow is shown to converge to a metric of constant scalar…

We produce complete bounded curvature solutions to K\"ahler-Ricci flow with existence time estimates, assuming only that the initial data is a smooth \K metric uniformly equivalent to another complete bounded curvature \K metric. We obtain…

This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…

In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to…

A formulation of the immersed boundary method for incompressible flow over bodies with surface slip described by the Navier boundary condition is presented. In the present method, the wall slip velocity and the boundary force are determined…