Related papers: A Maximum Principle for Combinatorial Yamabe Flow
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
In this work we extend the ODE Maximum principle of Hamilton to non-compact hypersurfaces using the Omari-Yau maximum principle at infinity. As an application of this result, we investigate Inverse Mean Curvature Flow (IMCF) of non-compact…
The aim of this work is twofold. From a mathematical point of view, we show the existence of a hyperbolic system of equations that is not symmetrizable in the sense of Friedrichs. Such system appears in the theory of compressible fluid…
We introduce a Yamabe-type flow \begin{align*} \left\{ \begin{array}{ll} \frac{\partial g}{\partial t} &=(r^m_{\phi}-R^m_{\phi})g \\ \frac{\partial \phi}{\partial t} &=\frac{m}{2}(R^m_{\phi}-r^m_{\phi}) \end{array} \right. ~~\mbox{ in }M…
Preservation of the maximum principle is studied for the combination of the linear finite element method in space and the $\theta$-method in time for solving time dependent anisotropic diffusion problems. It is shown that the numerical…
The prescribed scalar curvature flow was introduced to study the problem of prescribing scalar curvature on manifolds. Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study…
We study a class of fourth order curvature flows on a compact Riemannian manifold, which includes the gradient flows of a number of quadratic geometric functionals, as for instance the L2 norm of the curvature. Such flows can develop a…
There has been interest in finding a general variational principle for non-equilibrium statistical mechanics. We give evidence that Maximum Caliber (Max Cal) is such a principle. Max Cal, a variant of Maximum Entropy, predicts dynamical…
We present a new formulation of non-dissipative relativistic spin hydrodynamics that incorporates spin degrees of freedom into the divergence-type theory framework. Due to the divergence-type structure, it is straightforward to enforce…
In this paper, we prove a general maximum principle for the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we construct complete manifolds with…
In this paper we study the parabolic evolution equation $\partial_t u=(|Du|^{2}+2|\det Du|)^{-1} \Delta u$, where $u : M\times[0,\infty) \to N$ is an evolving map between compact flat surfaces. We use a tensor maximum principle for the…
Thurston's triangulation conjecture asserts that every hyperbolic 3-manifold admits a geometric triangulation into hyper-ideal hyperbolic tetrahedra. So far, this conjecture had only been proven for a few special 3-manifolds. In this…
In [12], the existence of ideal circle patterns in Euclidean or hyperbolic background geometry under the combinatorial conditions was proved using flow approaches. It remains as an open problem for the spherical case. In this paper, we…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
Formally self-adjoint, conformally covariant, polydifferential operators provide a general framework for studying variational problems, such as prescribing the scalar, $Q$-, or $\sigma_2$-curvatures, within a conformal class. We describe…
The non-modal self-heating mechanism driven by the velocity shear in kinematically complex magnetohydrodynamic (MHD) plasma flows is considered. The study is based on the full set of MHD equations including dissipative terms. The equations…
Three very different algorithms have been proposed for solution of the Rayleigh-Taylor turbulent mixing problem. They are based upon three different physical principles governing the Euler equations for fluid flow, which serve to complete…
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a…
In this paper we prove parabolic Schauder estimates for the Laplace-Beltrami operator on a manifold $M$ with fibered boundary and a $\Phi$-metric $g_\Phi$. This setting generalizes the asymptotically conical (scattering) spaces and includes…
Abstract approaches to maximum and anti-maximum principles for differential operators typically rely on the condition that all vectors in the domain of the operator are dominated by the leading eigenfunction of the operator. We study the…