arXiv research

We give a geometric interpretation of the linear trace Harnack inequality for the Ricci flow.

Quantum stochastic flow computes heat kernel traces for Ricci flat manifolds.

The paper surveys the Guillemin-Uribe trace formula for magnetic Laplacians.

We show a connection between the linear trace Li-Yau-Hamilton inequality for the Kaehler-Ricci flow and the monotonicity formula for the positive currents. As an application of the linear trace Li-Yau-Hamilton stated in this paper and the one proved by Chow-Hamiltonm, we give another proof on the classification of the …

Study geometric quantization of Hamiltonian flows using Berezin-Toeplitz operators.

Study of Hamiltonian flows on character varieties for self-intersecting curves.

New method tracks electricity flows to measure carbon emissions in real-time.

Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.

Guillemin trace formula adapted for group actions.

Ancient Ricci flows with nonnegative curvature operator have bounded entropy.

OT-Flow uses optimal transport to improve CNFs for faster and more accurate density estimation.

Improves modeling of sets with permutation invariant densities.

We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed geodesics. A corollary of this dynamical trace formula is a dynamical resonance-wave trac…

An important and natural question in the analysis of Ricci flow singularity formation in dimensions four and above is as follows: What are the weakest conditions that provide control of the norm of the Riemann curvature tensor? In this short note, we show that on a compact manifold, the trace-free Ricci tensor is contr…

Generative model for condensed matter using Riemannian flow matching.

We generalize Hamilton's matrix Li-Yau-type Harnack estimate for the Ricci flow by considering the space of all LYH (Li-Yau-Hamilton) quadratics that arise as curvature tensors of space-time connections satisfying the Ricci flow with respect to the natural space-time degenerate metric. As a special case, we employ scal…

A trace formula for foliated flows on closed manifolds.

We prove a linear trace Li-Yau-Hamilton inequality for the Kaehler-Ricci flow. We then use this sharp differential inequality to study the Liouville properties of the plurisubharmonic functions on complete Kaehler manifolds with nonnegative bisectional curvature.

Study gradient flow of phase transitions with fixed contact angle.

New gauge preserves Einstein metrics' interactions, proving rigidity on negatively curved manifolds.

Defines an equivariant Ruelle dynamical zeta function for flows on manifolds.

Flow maps into minimal surfaces with free boundary.

The main objective of the paper is to prove a geometric version of sharp trace and product estimates on null hypersurfaces with finite curvature flux. These estimates play a crucial role to control the geometry of such null hypersurfaces. The paper is based on an invariant version of the classical Littlewood -Paley the…

TRACE improves conformal prediction for multi-dimensional outputs.

Paper proves stability for recovering connections from holonomy traces.

In this note we investigate the behaviour at finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M^m_t\hookrightarrow (N^{m+n}, h). We show that they are characterized by the blow-up of a trace A = H \cdot II of the square of the second fundamental form.

Proof that certain Anosov flows are almost equivalent.

FlowGN tackles graph representation learning by tracing information flow paths.

We establish a one-parameter family of Harnack inequalities connecting the constrained trace Li-Yau differential Harnack inequality for a nonlinear parabolic equation to the constrained trace Chow-Hamilton Harnack inequality for this nonlinear equation with respect to evolving metrics related to Ricci flow on a 2-dimen…

Researchers prove spectral rigidity of Liouville tori under specific conditions.

Formula derived for zeta functions of 3D foliated systems.

Study improves Harnack estimates for porous medium equation under geometric flow.

Symplectic GP regression models Hamiltonian systems for particle tracing.

Study Floer theory of hyperbolic three-manifolds using Dirac spectral flow.

Finite-time blow-up in Yang-Mills flow for small energy initial connections.

In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact 3-manifold is path-connected. The proof uses the Ricci flow with surgery, the conformal method, and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilton's Ricci flow is fundam…

Method extracts taint flows to classify Bitcoin mining pools.

Study reveals how to determine area and curvature from fluid flow resonances.

Study of curvature tensor algebra with nonstandard multiplications.

We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for…

The paper studies special Lagrangian submanifolds in complex spaces and derives inequalities and flow methods.

We prove constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation $ω_t=Δω+aω\ln ω$ on closed manifolds. We also derive a new interpolated Harnack inequality for the equation $ω_t=Δω-ω\lnω+\varepsilon Rω$ on closed surfaces under the $\varepsilon$-Ricci flow. Finally we prove…

In his approach to analytic number theory C. Deninger has suggested that to the Riemann zeta function $\hatζ(s)$ (resp. the zeta function $ζ_Y(s)$ of a smooth projective curve $Y$ over a finite field $\mathbb{F}_q$, $q=p^f$)) one could possibly associate a foliated Riemannian laminated space $(S_{\mathbb{Q}}, \mathcal{…

Let $M$ be a closed Riemannian manifold with a family of Riemannian metrics $g_{ij}(t)$ evolving by a geometric flow $\partial_{t}g_{ij} = -2{S}_{ij}$, where $S_{ij}(t)$ is a family of smooth symmetric two-tensors. We derive several differential Harnack estimates for positive solutions to the nonlinear backward heat-ty…

New linear flows using exponential of linear transformations improve generative models.

A map from 3-manifold skein to Lagrangian skein via holomorphic curve counting.

Paper presents a new method to detect process differences at the trace level using mutual fingerprints.

Let $M$ be a closed Riemannian manifold with a family of Riemannian metrics $g_{ij}(t)$ evolving by geometric flow $\partial_{t}g_{ij} = -2{S}_{ij}$, where $S_{ij}(t)$ is a family of smooth symmetric two-tensors on $M$. In this paper we derive differential Harnack estimates for positive solutions to the nonlinear heat …