Related papers: The Markov property for $\varphi^4_3$ on the cylin…

We prove gradient bounds for the Markov semigroup of the dynamic $\varphi^4_2$-model on a torus of fixed size $L>0$. For sufficiently large mass $m>0$ these estimates imply exponential contraction of the Markov semigroup. Our method is…

We prove an a priori bound for the dynamic $\Phi^4_3$ model on the torus wich is independent of the initial condition. In particular, this bound rules out the possibility of finite time blow-up of the solution. It also gives a uniform…

We study invariant boundary conditions for one dimensional discrete Gaussian Markov processes, basic toy models of spatial Markov processes in statistical mechanics. More precisely, we give a decomposition of boundary objects in a non…

We generalize to some PDEs a theorem by Nekhoroshev on the persistence of invariant tori in Hamiltonian systems with $r$ integrals of motion and $n$ degrees of freedom, $r\leq n$. The result we get ensures the persistence of an…

We show that there is a good notion of irreducible sympelectic varieties of $\mathrm{K3}^{[n]}$-type over an arbitrary field of characteristic zero or $p > n + 1$. Then we construct mixed characteristic moduli spaces for these varieties.…

In this paper the problem of persistence of invariant tori under small perturbations of integrable Hamiltonian systems is considered. The existence of one-to-one correspondence between hyperbolic invariant tori and critical points of the…

In this paper we study the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi's iteration. As applications, we show the existence of weak solutions for possibly degenerate stochastic…

This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the…

We establish several boundary $\varepsilon$-regularity criteria for suitable weak solutions for the 3D incompressible Navier-Stokes equations in a half cylinder with the Dirichlet boundary condition on the flat boundary. Our proofs are…

We constructed in a previous work the $\Phi^4_3$ measures on compact boundaryless $3$-dimensional Riemannian manifolds as some invariant probability measures of some Markovian dynamics. We prove in the present work that these dynamics have…

We construct the Dirichlet form associated with the dynamical $\Phi^4_3$ model obtained in [Hai14, CC13] and [MW16]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this…

We realize explicit symmetries of Bridgeland stability conditions on any abelian threefold given by Fourier-Mukai transforms. In particular, we extend the previous joint work with Maciocia to study the slope and tilt stabilities of sheaves…

The continuum $\varphi^4_2$ and $\varphi^4_3$ measures are shown to satisfy a log-Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that their susceptibility is bounded. In particular, this applies to…

We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and…

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid…

We develop a general method to prove the existence of spectral gaps for Markov semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for this analysis is neither a weighted supremum norm nor an ${\L}^p$-type…

We construct and study the unique random tiling of the hyperbolic plane into ideal hyperbolic triangles (with the three corners located on the boundary) that is invariant (in law) with respect to Moebius transformations, and possesses a…

We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are…

In this paper we study the 3-dimensional $(\varepsilon) $-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\varepsilon ) $-para Sasakian 3 -manifold to be an indefinite space form. We show that a…

Let $n\geq 4$. In this paper, we construct a sequence of smooth Riemannian metrics $g_i $ on $\mathbb{R}^n$ such that: (1) $g_i = g_{\rm Euc} $ outside the standard Euclidean unit ball $B_1 (0) \subset \mathbb{R}^n $, (2) ${\rm Ric}_{g_i}…