arXiv research

In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating m…

Study proves existence and properties of shrinkers in area-preserving curve-shortening flow.

Extends Hard Lefschetz Property to isometric flows and shows equivalence.

Paper shows regularizing flow for conical Kähler-Ricci equations.

We study the properties of Modified Riemann extensions evolving under Ricci flow. We obtain the necessary and sufficient condition for modified Riemann extension under Ricci flow to stay as modified Riemann extension. We also discuss the properties of the curvature tensors under Ricci flow.

Jointly estimates flow fields and particle properties from Lagrangian data.

We prove a so called $κ$ non-inflating property for Ricci flow, which provides an upper bound for volume ratio of geodesic balls over Euclidean ones, under an upper bound for scalar curvature. This result can be regarded as the opposite statement of Perelman's $κ$ non-collapsing property for Ricci flow. These two resul…

Heat flow fails to preserve concavity in curved spaces.

Alexandrov immersed surfaces maintain their properties under mean curvature flow.

Stability of Type IIA flow ensures Kähler properties of Calabi-Yau 3-folds.

Harmonic map flow's singularity properties proven with Lojasiewicz inequalities.

The rectified flow method is analyzed for its statistical properties.

We prove that a general complex Monge-Ampère flow on a Hermitian manifold can be run from an arbitrary initial condition with zero Lelong number at all points. Using this property, we confirm a conjecture of Tosatti-Weinkove: the Chern-Ricci flow performs a canonical surgical contraction. Finally, we study a generaliza…

Study of Anosov flows using microlocal analysis for ergodicity and mixing properties.

Flow on weighted graphs sharpens Bakry-Émery curvature.

We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a concavity maximum principle argument to the corresponding level set f…

In this note, we combine the work of Ilmanen and of Colding-Ilmanen-Minicozzi to observe a uniqueness property for tangent flows at the first singular time of a smooth mean curvature flow of a closed surface in 3-dimensional Euclidean space. Specifically, if, at a fixed singular point, one tangent flow is a positive in…

We consider flows, called $W^{\rm u}$ flows, whose orbits are the unstable manifolds of a codimension one Anosov flow. Under some regularity assumptions, we give a short proof of the strong mixing property of $W^{\rm u}$ flows and we show that $W^{\rm u}$ flows have purely absolutely continuous spectrum in the orthocom…

We study the regularizing properties of complex Monge-Ampère flows on a Kähler manifold $(X,ω)$ when the initial data are $ω$-psh functions with zero Lelong number at all points. We prove that the general Monge-Ampère flow has a solution which is immediately smooth. We also prove the uniqueness and stability of solutio…

Let $Ω$ be a compact Riemannian manifold with smooth boundary and let $u_t$ be the solution of the heat equation on $Ω$, having constant unit initial data $u_0=1$ and Dirichlet boundary conditions ($u_t=0$ on the boundary, at all times). If at every time $t$ the normal derivative of $u_t$ is a constant function on the …

The paper studies knots in modular flows using self-covers.

Geodesic completeness and flow properties of compact Brinkmann spacetimes proven.

The paper studies curve shortening flows on non-convex surfaces.

Flow preserves curvature sharpness on weighted graphs.

The paper proves new inequalities and flow properties for hypersurfaces.

We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for the combinatorial one and that, moreover, the same results hold for a more gene…

Study on droplet flow on uneven surfaces, proving existence and properties.

Novel Ricci flow normalization for homogeneous spaces, focusing on flag manifolds.

We show the convergence properties of the eigenvalues of the Dirac operator on a spin manifold with a Riemannian flow when the metric is collapsed along the flow.

New surgery method preserves Anosov flow properties using bi-contact geometry.

To every Ricci flow on a manifold M over a time interval I, we associate a shrinking Ricci soliton on the space-time M x I. We relate properties of the original Ricci flow to properties of the new higher-dimensional Ricci flow equipped with its own time-parameter. This geometric construction was discovered by considera…

Study dynamics and topology of flows near non-saddle sets or W-sets.

Incorporates matrix exponential into generative flows for improved performance.

Study preserves planar and graphical properties of curves under elastic flow.

Study XRP network, propose Flow Index to analyze transaction frequencies.

ESS-Flow guides flow models without retraining, using Bayesian inference in source space.

Study on Gaussian interpolation flows for generative modeling.

This paper studies gradient flows for sampling using various metrics and their affine invariance.

We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. We consider the behavior of Ricci flow with surgery starting from a fixed initial compact Riemannian 3-manifold, as the surgery parameter varies. We prove that the flow with surgery subconverges to a singular Ri…

The paper explores the geometric properties of fluid flows and their symmetries.

We simplify and improve the curvature estimates in the paper: On the conditions to extend Ricci flow(II). Furthermore, we develop some volume estimates for the Ricci flow with bounded scalar curvature. These estimates can be applied to study the singularities of the Ricci flow and convergence properties of the Kähler R…

New model predicts radiative properties of nanoparticle layers with high accuracy and uncertainty.

We investigate the ability of popular flow based methods to capture tail-properties of a target density by studying the increasing triangular maps used in these flow methods acting on a tractable source density. We show that the density quantile functions of the source and target density provide a precise characterizat…

The paper proves geometric inequalities in sphere using locally constrained flows.

The paper studies mean curvature flow in a Ricci flow background with extended Ricci flow.

Method for conditional sampling with pre-trained normalizing flows.

In this paper, we study the convexity, interior gradient estimate, Liouville type theorem and asymptotic behavior at infinity of translating solutions to mean curvature flow as well as the nonlinear flow by powers of the mean curvature.

New method for modeling densities on Riemannian manifolds with symmetries.