arXiv research

The article characterizes gradient ρ-Einstein solitons under specific conditions.

Study geometric and topological properties of Finsler manifolds with weighted Ricci curvature bounds.

In this paper we consider the Ricci curvature of a Ricci soliton. In particular, we have showed that a complete gradient Ricci soliton with non-negative Ricci curvature possessing a non-constant convex potential function having finite weighted Dirichlet integral satisfying an integral condition is Ricci flat and also i…

WBCP improves conformal prediction for distribution shifts using weighted Dirichlet posteriors.

Study extends eigenvalue formulas to weighted manifolds and proves global rigidity theorems.

Sharp bounds for Dirichlet sums lead to improved Bayesian algorithm analysis.

Study on a weighted Suita conjecture for higher derivatives and their geometric properties.

A new method uses a product of experts with Dirichlet variables to approximate complex distributions.

This paper introduces a deep learning ensemble forecasting model using Dirichlet process.

We propose a deterministic numerical method for pricing vanilla options under the SABR stochastic volatility model, based on a finite element discretization of the Kolmogorov pricing equations via non-symmetric Dirichlet forms. Our pricing method is valid under mild assumptions on parameter configurations of the proces…

Study connects curvature to graph theory and reveals differences.

We discuss optimal lower bounds for eigenvalues of Laplacians on weighted graphs. These bounds are formulated in terms of the geometry and, more specifically, the inradius of subsets of the graph. In particular, we study the first non-zero eigenvalue in the finite volume case and the first eigenvalue of the Dirichlet L…

Quadratic differentials on Riemann surfaces uniquely determine foliations.

Efficiently approximates uncertainty in classification models using Dirichlet distributions.

The paper characterizes solitons and estimates scalar curvature.

Study compares nonsmooth spaces with integrable Ricci bounds.

We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically, we show that such a solution can be approximated by integrals over finite-dimens…

The paper analyzes Laplace learning for Gaussian measure data in infinite dimensions, proving convergence.

New portfolios outperform traditional methods by using factor weights.

We consider a compact Riemann surface $R$ of arbitrary genus, with a finite number of non-overlapping quasicircles, which separate $R$ into two subsets: a connected Riemann surface $Σ$, and the union $\mathcal{O}$ of a finite collection of simply-connected regions. We prove that the Schiffer integral operator mapping t…

Gradient estimate for harmonic functions with boundary condition proved.

Solves constant mean curvature Dirichlet problem on catenoids with improved estimates.

The paper defines Dirichlet domains for Anosov subgroups in Lie groups.

Dirichlet-Neumann duality for Riemannian submersions

We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed homotopy class and all hyperbolic metrics on the surface. We give explicit example…

Prove top wedge power of Ricci form has finite integral for Kähler manifolds with positive sectional curvature

Study on Dirichlet process mixtures for clustering consistency.

We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of "weight systems", finding everything to be in agreement with the conjecture that "every weight system integrates".

The paper explores inequalities between eigenvalues on Riemannian manifolds.

The Poisson equation on manifolds plays an fundamental role in many applications. Recently, we proposed a novel numerical method called the Point Integral method (PIM) to solve the Poisson equations on manifolds from point clouds. In this paper, we prove the convergence of the point integral method for solving the Pois…

We consider noncompact complete manifolds with Spin(9) holonomy and proved an one end result and a splitting type theorem under different conditions on the bottom of the spectrum. We proved that any harmonic functions with finite Dirichlet integral must be Cayley-harmonic, which allowed us to conclude an one end result…

Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over Dirichlet parameters complicate the joint distribution of model parameters. This paper s…

In this work we study the intrinsic geometry of the space of Kahler metrics under various Riemannian metrics. The first part is on the Dirichlet metric. We motivate its study, we compute its curvature, and we make links with the Calabi metric, the K-energy, the degenerate complex Hessian equation. The second part is on…

The aim of this text is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of hyperplanes. We deduce from these relations and the computation of the connexion obtained by moving one hyperplane of th…

The paper proposes a new method for covariate balancing using IPM to improve causal inference.

Paper proves stability and Dirichlet problem for translating hypersurfaces.

We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, sharp gradient and Hessian estimates are derived for the Dirichlet and Neumann eigenfunctions.

Counting HCMU sphere components using weighted trees.

Estimates the mass gap for domains with integral Ricci curvature bounds.

We introduce higher-order Poincar'e constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue of the $p$-Laplacian. In the case of the closed eigenvalue problem and the Neuma…

A new method detects outliers using ensembles of Dirichlet process mixtures.

Estimates eigenvalues on weighted manifolds with curvature.

Study inequalities involving torsional rigidity and spherical deficit on Riemannian manifolds.

The paper finds metrics for surfaces with boundaries that match specific eigenvalues and areas.

We prove that if $N\ge 2$ and $α: F_N\to π_1(Γ)$ is a marking on $F_N$, then for any integer $r\ge 2$ and any $F_N$-invariant collection of non-negative integral "weights" associated to all subtrees $K$ of $\widetilde Γ$ of radius $\le r$ satisfying some natural "switch" conditions, there exists a finite cyclically red…

A new method for density estimation using nearest neighbor Dirichlet mixtures.

Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.

Corrected moment-based methods improve inference in topic model regression.