Related papers: A fractional Yamabe flow and some applications

Using the fractional discrete Laplace operator for triangle meshes, we introduce a fractional combinatorial Calabi flow for discrete conformal structures on surfaces, which unifies and generalizes Chow-Luo's combinatorial Ricci flow for…

A floating hemisphere under forced harmonic oscillation at very high and very low frequencies is considered. The problem is reduced to an elliptic one, that is, the Laplace operator in the exterior domain with standard Dirichlet and Neumann…

We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional $Q$-curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of…

We prove an escape rate result for special semi-flows over non-invertible subshifts of finite type. Our proofs are based on a discretisation of the flow and an application of an escape rate result for conformal repellers.

We give a survey of various compactness and non-compactness results for the Yamabe equation. We also discuss a conjecture of Hamilton concerning the asymptotic behavior of the parabolic Yamabe flow.

A combinatorial version of Yamabe flow is presented based on Euclidean triangulations coming from sphere packings. The evolution of curvature is then derived and shown to satisfy a heat equation. The Laplacian in the heat equation is shown…

We prove global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation we consider generalizes two-sphere-valued completely integrable systems…

The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4-manifolds. In addition, we provide topological sphere theorems for compact…

We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection…

In this paper, we derive several regularity results for harmonic mappings into Euclidean spheres associated with rather general energies related to fractional Sobolev spaces. These maps generalize families of maps introduced by Da Lio,…

In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…

In the limit of a nonlinear diffusion model involving the fractional Laplacian we get a "mean field" equation arising in superconductivity and superfluidity. For this equation, we obtain uniqueness, universal bounds and regularity results.…

We consider the volume constrained fractional mean curvature flow of a nearly spherical set, and prove long time existence and asymptotic convergence to a ball. The result applies in particular to convex initial data, under the assumption…

In this paper we consider the functional whose critical points are solutions of the fractional CR Yamabe type equation on the sphere. We firstly study the behavior of the Palais-Smale sequences characterizing the bubbling phenomena and…

We study the Yamabe flow on compact Riemannian manifolds of dimensions greater than two with minimal boundary. Convergence to a metric with constant scalar curvature and minimal boundary is established in dimensions up to seven, and in any…

Let $(X^{n+1}, g^+)$ be an $(n+1)$-dimensional asymptotically hyperbolic manifold with a conformal infinity $(M^n, [\hat{h}])$. The fractional Yamabe problem addresses to solve \[P^{\gamma}[g^+,\hat{h}] (u) = cu^{n+2\gamma \over n-2\gamma},…

This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…

Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal curvature flow for convex closed plane curves and discuss the short time existence and asymptotic convergence behavior of the flow. Due to the linear structure…

We consider the inverse mean curvature flow by parallel hypersurfaces in space forms. We show that such a flow exists if and only if the initial hypersurface is isoparametric. The flow is characterized by an algebraic equation satisfied by…

A kind of problems of radially symmetric transient fluid flow in a medium with a geometry similar to a hollow-disk can be addressed using the finite Hankel transform. However, the inverse Hankel transform [G. Cinelli, Int. J. Engng. Sci.,…