arXiv research

This paper proves Hölder continuity for complex Monge-Ampère equations on Kähler varieties.

Study continuity and Hölder estimates for solutions on Stein spaces.

Study on Kähler-Ricci flow's Hölder regularity on compact manifolds.

New method improves curvature estimates for stable surfaces.

The paper proves Hölder continuity for solutions of degenerate parabolic equations in any dimension.

We analyze the Kozachenko--Leonenko (KL) nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance over Hölder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a new minimax lower bound over the Hölder ba…

Gradient-free optimization for additive models achieves optimal error.

Optimal nonparametric regression estimator adapts to unknown smoothness.

This paper bounds the volume of singular and critical sets for elliptic equations with Hölder coefficients.

This is a note on \cite{LSU} and \cite{FS}. Using their work line by line, we prove the Hölder-continuity of solutions to linear parabolic equations of mixed type, assuming the coefficient of $\frac{\partial}{\partial t}$ has time-derivative bounded from above. On a Kähler manifold, this Hölder estimate works when the …

The paper bounds the expectation of empirical processes indexed by Hölder classes.

Paper proposes deep neural networks for nonparametric regression from dependent data.

The paper converts metric bounds to distance function Hölder bounds and proves compactness theorems.

Develops a deep learning framework for various data types.

We give a proof that Brakke's mean curvature flow under the unit density assumption is smooth almost everywhere in space-time. More generally, if the velocity is equal in a weak sense to its mean curvature plus some given α-Hölder continuous vector field, then we show C^{2,α} regularity almost everywhere.

A canonical diffeomorphism is constructed for manifolds near spheres.

Bounds on treatment effect sensitivity in causal reasoning using Hölder's inequality.

The paper improves estimates for asymptotically hyperbolic Einstein manifolds in even dimensions.

Neural networks with integer weights approximate continuous functions efficiently.

Reverse Hölder inequalities on Fano metrics with applications to geodesics and singularities.

We show that normalized currents of integration along the common zeros of random $m$-tuples of sections of powers of $m$ singular Hermitian big line bundles on a compact Kähler manifold distribute asymptotically to the wedge product of the curvature currents of the metrics. If the Hermitian metrics are Hölder with sing…

New statistical framework for coresets in density estimation.

Extends boundary estimates for Monge-Ampère equations in polygonal domains.

Develops regularity theory for Beckmann's optimal transport problem.

New stability estimate for metric rigidity in hyperbolic dynamics.

Study asymptotic behavior of second Chern forms on degenerating Kähler-Einstein surfaces.

New method efficiently interpolates nonparametric density estimators.

The study proves inequalities for complex operators on curved spaces.

Study explores relationship between Hölder and FDPD divergences.

Deep neural networks without regularization can achieve consistent estimates with good convergence rates.

New Holder bounds improve variational inference by flattening thermodynamic curves.

In statistical analysis, measuring a score of predictive performance is an important task. In many scientific fields, appropriate scores were tailored to tackle the problems at hand. A proper score is a popular tool to obtain statistically consistent forecasts. Furthermore, a mathematical characterization of the proper…

We prove the Livšic Theorem for arbitrary $GL(m,\mathbb R)$ cocycles. We consider a hyperbolic dynamical system $f : X \to X$ and a Hölder continuous function $A: X \to GL(m,\mathbb R)$. We show that if $A$ has trivial periodic data, i.e. $A(f^{n-1} p) ... A(fp) A(p) = Id$ for each periodic point $p=f^n p$, then there …

Improved estimators for causal inference using cross-fitting and undersmoothing.

Develops analysis of Hölder continuous mappings on Heisenberg groups.

Proves Hölder continuity of complex Monge-Ampère solutions.

New algorithm improves matrix estimation with one-sided covariates.

Proves rigidity of maps between balls with Hölder boundary continuity.

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

Paper analyzes deep neural networks with dependent data, establishing convergence rates and error bounds.

Study bounds Kähler current diameters on manifolds.

Study nonparametric density estimation via measure transport, achieving optimal rates.

Adapts Hölder smoothness with normalized gradients.

The paper tackles deep learning from dependent data, achieving optimal performance.

We define a generalization of convex functions, which we call $δ$-convex functions, and show they must satisfy interior Hölder and $W^{1,p}$ estimates. As an application, we consider solutions of a certain class of fully nonlinear equations in conformal geometry with isolated singularities, in the case of non-negative …

Develops uniform convergence guarantees for a broad class of risk functionals in supervised learning.

Quasiregular curves are Hölder continuous and have higher integrability.

Transformer networks approximate Hölder and Sobolev functions with fixed-depth networks.