相关论文: Estimates and monotonicity for a heat flow of isom…

In this paper, we study the stability two-dimensional (2D) steady Euler flows with sharply concentrated vorticity in a simply-connected bounded domain. These flows are obtained as maximizers of the kinetic energy subject to the constraint…

On a smooth closed oriented 4-manifold $M$ with a smooth action by a finite group $G$, we show that a $G$-monopole class gives the $L^2$-estimate of the Ricci curvature of a $G$-invariant Riemannian metric, and derive a topological…

Statistical mechanics provides an elegant explanation to the appearance of coherent structures in two-dimensional inviscid turbulence: while the fine-grained vorticity field, described by the Euler equation, becomes more and more filamented…

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…

We show that H\"{o}lder continuous incompressible Euler flows that satisfy the local energy inequality ("globally dissipative" solutions) exhibit nonuniqueness and contain examples that strictly dissipate kinetic energy. The collection of…

We construct new compact manifolds endowed with closed $\mathrm{G}_2$ structures that satisfy the topological properties found by Joyce and Baraglia for the existence of a torsion-free $\mathrm{G}_2$ structure in the same cohomology class.…

We prove a monotonicity formula for mean curvature flow with surgery. This formula differs from Huisken's monotonicity formula by an extra term involving the mean curvature. As a consequence, we show that a surgically modified flow which is…

We prove the mean curvature flow of a spacelike graph in $(\Sigma_1\times \Sigma_2, g_1-g_2)$ of a map $f:\Sigma_1\to \Sigma_2$ from a closed Riemannian manifold $(\Sigma_1,g_1)$ with $Ricci_1> 0$ to a complete Riemannian manifold…

We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…

We establish effective existence and uniqueness for the heat flow on time-dependent Riemannian manifolds, under minimal assumptions tailored towards the study of Ricci flow through singularities. The main point is that our estimates only…

We study the gradient flow lines of a Yang-Mills-type functional on the space of gauged holomorphic maps $\mathcal{H}(P,X)$, where $P$ is a principal bundle on a Riemann surface $\Sigma$ and $X$ is a K\"ahler Hamiltonian $G$-manifold. For…

In this paper we investigate the properties of rapidly rotating decaying turbulence using numerical simulations and phenomenological modelling. We find that as the turbulent flow evolves in time, the Rossby number decreases to $\sim…

Hydrodynamics describes the evolution of macroscopic states in non--equilibrium thermodynamics. Following Onsager reciprocal relations, one can formulate a large class of hydrodynamic equations as gradient flows of free energies. In recent…

We study the positive Hermitian curvature flow of left-invariant metrics on complex 2-step nilpotent Lie groups. In this setting we completely characterize the long-time behaviour of the flow, showing that normalized solutions to the flow…

Part I of this paper presented a systematic derivation of the Stokes Dirac structure underlying the port-Hamiltonian model of ideal fluid flow on Riemannian manifolds. Starting from the group of diffeomorphisms as a configuration space for…

The fixed points of the generalized Ricci flow are the Bismut Ricci flat metrics, i.e., a generalized metric $(g,H)$ on a manifold $M$, where $g$ is a Riemannian metric and $H$ a closed $3$-form, such that $H$ is $g$-harmonic and…

In this article we investigate the dynamical properties of the geodesic flow for a proper metric space endowed with a proper action by isometries of a group with a contracting element. We show that the existence of a contracting isometry is…

We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…

We compute the one- and two-loop RG flow of integrable $\sigma$-models with Poisson-Lie symmetry. They are characterised by a twist function with $2N$ simple poles/zeros and a double pole at infinity. Hence, they capture many of the known…

Let $M$ be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian $H:T^*M\rightarrow \mathbb R$ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits…