arXiv research

Kahler-Ricci flow long-time behavior and initial data

Study an anisotropic capillary flow to solve capillary Orlicz-Minkowski problem.

Proves long-term smoothness of curved surfaces evolving under specific curvature rules.

The paper proves smoothness of mean curvature flow for generic initial data in 3D and 4D.

Study shows Ricci flow's convergence and harmonic map heat flow's long-time existence.

Proves long-time Ricci flow existence and topological rigidity for pinched integral curvature manifolds.

We describe some relations between the long-time asymptotic behavior of the vacuum Einstein evolution equations and the geometrization of 3-manifolds. These relations are expressed in terms of evolution of CMC hypersurfaces in the vacuum space-time.Some results are also obtained on the singularity avoidance of CMC foli…

In this paper, we prove that if an asymptotically Euclidean manifold $(M^n,g)$ under the condition that $R \ge 0$ has long time existence of Ricci flow, the mass of $(M^n,g)$ is nonnegative. In addition, we give an independent proof of positive mass theorem in dimension $3$.

The paper studies a specific centro-affine invariant hypersurface flow in R^(n+1).

We consider the long-time behaviour of the mean curvature flow of spacelike hypersurfaces in the Lorentzian product manifold $M\times\mathbb{R}$, where $M$ is asymptotically flat. If the initial hypersurface $F_0\subset M\times\mathbb{R}$ is uniformly spacelike and asymptotic to $M\times\left\{s\right\}$ for some $s\in…

We determine the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a Robertson-Walker space-time. We prove in particular that when approaching the explosion time of the diffusion, its projection on the base manifold almost surely converges to a random point of the …

Study refracted skew Brownian motion, find densities and asymptotics.

This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as l…

Study on consensus formation in manifolds with curvature constraints.

As part of the general investigation of Ricci flow on complete surfaces with finite total curvature, we study this flow for surfaces with asymptotically conical (which includes as a special case asymptotically Euclidean) geometries. After establishing long-time existence, and in particular the fact that the flow preser…

The paper studies 1-equivariant harmonic map flow behavior from R² to S².

We study the Ricci flow on complete Kaehler metrics that live on the complement of a divisor in a compact complex manifold. In earlier work, we considered finite-volume metrics which, at spatial infinity, are transversely hyperbolic. In the present paper we consider three different types of spatial asymptotics: cylind…

By making use of the nice behavior of Hawking masses of slices of a weak solution of inverse mean curvature flow in three dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of the flow is star-shaped after a long time, and then we get the regularity of the weak solution of inverse mean…

Study shows global oscillatory solutions for Yang-Mills heat flow in 4D space.

The paper studies heat behavior on curved spaces without radiality assumption.

New theorem shows curvature concentration depends linearly on volume ratio.

We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with …

This work analyzes a two-stage algorithm for single index models, showing precise asymptotics of gradient descent.

Constructs constant spacetime mean curvature surfaces for hyperboloidal initial data sets.

Study of prescribed mean curvature flow on noncompact hypersurfaces in Lorentz manifolds.

We study long-time existence and asymptotic behaviour for a class of anisotropic, expanding curvature flows. For this we adapt new curvature estimates, which were developed by Guan, Ren and Wang to treat some stationary prescribed curvature problems. As an application we give a unified flow approach to the existence of…

We study the mean curvature flow of complete space-like submanifolds in pseudo-Euclidean space with bounded Gauss image, as well as that of complete submanifolds in Euclidean space with convex Gauss image. By using the confinable property of the Gauss image under the mean curvature flow we prove the long time existence…

We obtain an estimate from below for the remainder in Weyl's law on negatively curved surfaces. In the constant curvature case, such a bound was proved independently by Hejhal and Randol in 1976 using the Selberg zeta function techniques. Our approach works in arbitrary negative curvature, and is based on wave trace as…

The paper studies constant harmonic mean curvature surfaces in Schwarzschild spaces, proving they foliate the space.

Stability of a special spacetime solution is proven under certain symmetries.

We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the boundaries of the no-trade-region and the asymptotic optimal growth rate, which can be …

Study anisotropic flows without global terms and solve dual Orlicz Christoffel-Minkowski problems.

Study of tori of revolution under Willmore flow converges to Clifford Torus.

Study on how non-reversible diffusion processes affect homology on manifolds.

Study flows for capillary Minkowski problems in half-spaces.

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 hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over …

Study anisotropic inverse Gauss curvature flows and solve dual Orlicz Minkowski problems.

In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general cone angle and show that this solution has the optimal regularity, namely, the ti…

This is the first of a series of papers on the long-time behavior of 3 dimensional Ricci flows with surgery. In this paper we first fix a notion of Ricci flows with surgery, which will be used in this and the following three papers. Then we review Perelman's long-time estimates and generalize them to the case in which …

We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a Wishart process. This class extends the very popular Heston model to the multivariate …

Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of the process, penalized by an $\ell^1$-penalization (Lasso and Adaptive Lasso). …

In this paper, we study the positive cross curvature flow on locally homogeneous 3-manifolds. We describe the long time behavior of these flows. We combine this with earlier results concerning the asymptotic behavior of the negative cross curvature flow to describe the two sided behavior of maximal solutions of the cro…

This paper proves long-time accuracy of ensemble Kalman filters for chaotic and machine-learned systems.

Geometric focusing affects dispersive estimates for Schrödinger and wave equations.

Study knot singularities in Bogomolny equation solutions.

The paper studies how surfaces evolve in a cone under a specific flow.

Prove long-time existence of pluriclosed flow on certain fibrations

New criteria for long-time existence of parabolic flow from 11D supergravity.