arXiv research

Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.

Study approximates unknown function levels with queries.

We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact K{ä}hler manifolds. We characterize toric qpsh functions and give necessary and sufficient conditions for them to have finite (weighted) energy, both in terms of the associated convex function in R n , and through t…

The purpose of these notes is to explain parts of Gromov's survey of Carnot-Carathedory spaces, in the light of subsequent results of M. Rumin. Among the rich material provided by Gromov, most of which pertains to analysis on metric spaces, we choose to concentrate on the H{ö}lder equivalence problem for Carnot manifol…

We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\t…

Efficient algorithms for contextual bandits with smooth regret in continuous action spaces.

A variant of Gromov's H{ö}lder-equivalence problem, motivated by a pinching problem in Riemannian geometry, is discussed. A partial result is given. The main tool is a general coarea inequality satisfied by packing energies of maps.

In this paper we provide an alternative framework to tackle the first-best Principal-Agent problem under CARA utilities. This framework leads to both a proof of existence and uniqueness of the solution to the Risk-Sharing problem under very general assumptions on the underlying contract space. Our analysis relies on an…

In the context of stochastic continuum-armed bandits, we present an algorithm that adapts to the unknown smoothness of the objective function. We exhibit and compute a polynomial cost of adaptation to the H{ö}lder regularity for regret minimization. To do this, we first reconsider the recent lower bound of Locatelli an…

Let $S$ be a closed oriented surface of genus at least $2$, and denote by $\mathcal{T}(S)$ its Teichm{ü}ller space. For any isotopy class of closed curves $γ$, we compute the first three derivatives of the length function $\ell\_γ:\mathcal{T}(S)\rightarrow\mathbf{R}\_+$ in the shearing coordinates associated to a maxim…

We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive fashion by Rakhlin and Sridharan (2014). Our regret bound is expre…

Validates economic scenarios using statistical tests on stochastic processes.

Total curvatures of certain hypersurfaces are continuous.

Estimates curvature for long-time continuity method solutions.

Study on curvature blow-up and convergence of continuity method on Hirzebruch surface.

Proves existence of curved surfaces in hyperbolic space.

New methods for calculating curvature in graph theory.

Study shows continuous evolution of curves in Fréchet distance.

Estimates for Schrödinger operators on manifolds with bounded Ricci curvature.

Study shows zero-shot super-resolution in neural operators is impossible in many cases.

Study proves finiteness for distance functions on curved surfaces with controlled curvature.

3D metrics get scalar curvature bounds via IMCF.

Study biharmonic hypersurfaces in spheres, proving unique continuation theorem.

Convex solutions to a specific equation are smooth when the phase is smooth enough.

Let $M$ be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of $M$ is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatur…

Proposes a new model to identify unknown counterfactual outcomes for continuous variables.

Study shows uniform decay rate for singular mean curvature flows.

Continuous curve evolution depends on initial shape on sphere.

Proposes a weaker version of Strong Cosmic Censorship with curvature bounds.

New method proves absolute continuity of Wasserstein barycenters on manifolds with lower Ricci curvature bound.

Paper proves mass theorems for nonnegative scalar curvature metrics.

It is proved that solutions of the complex Monge-Ampère equation on compact Kähler manifolds with right hand side in $L^p, p>1$ are uniformly Hölder continuous under the assumption on non-negative orthogonal bisectional curvature.

Counterexamples to continuity of optimal transportation on Riemannian manifolds with everywhere positive sectional curvature are provided. These examples show that the condition A3w of Ma, Trudinger, & Wang is not guaranteed by positivity of sectional curvature.

Analytic plane curves determine unique conformal coordinates.

Using a method introduced by R. Bamler to study the behavior of scalar curvature under continuous deformations of Riemannian metrics, we prove that if a sequence of smooth Riemannian metrics gi on a fixed compact manifold M has isotropic curvature bounded from below by a nonnegative function u, and if gi converge in C …

In this paper we analyze the behavior of the distance function under Ricci flows whose scalar curvature is uniformly bounded. We will show that on small time-intervals the distance function is $\frac12$-Hölder continuous in a uniform sense. This implies that the distance function can be extended continuously up to the …

Proves convergence of mean curvature flow on cylinders with unique continuation.

The paper connects curvature positivity to rational connectedness in complex geometry.

The study proves the existence of $k$-convex hypersurfaces for specific curvature equations.

The paper proves estimates for Hermitian metrics and shows curvature blow-up on complex manifolds.

In 1997, J. Jost [27] and F. H. Lin [39], independently proved that every energy minimizing harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov space with non-positive curvature is locally Hölder continuous. In [39], F. H. Lin proposed a challenge problem: Can the Hölder continuity …

Study on special Lagrangian curvature potential equation, proving existence and uniqueness of smooth solutions.

In this paper, we continue studying the 6-dimensional pseudo-Riemannian space V^6(g_{ij}) with signature [++--], which admits projective motions, i. e. continuous transformation groups preserving geodesics. In particular, we determine a necessary and sufficient condition that the 6-dimensional rigid h-spaces have const…

Unique continuation results are proved for metrics with prescribed Ricci curvature in the setting of bounded metrics on compact manifolds with boundary, and in the setting of complete, conformally compact metrics. Related to this issue, an isometry extension property is proved: continuous groups of isometries at confor…

In this note we continue the analysis of metric measure space with variable ricci curvature bounds. First, we study $(κ,N)$-convex functions on metric spaces where $κ$ is a lower semi-continuous function, and gradient flow curves in the sense of a new evolution variational inequality that captures the information that …

The study examines continuous mean curvature functions on manifolds without conjugate points.

We construct new homogeneous Einstein spaces with negative Ricci curvature in two ways: First, we give a method for classifying and constructing a class of rank one Einstein solvmanifolds whose derived algebras are two-step nilpotent. As an application, we describe an explicit continuous family of ten-dimensional Einst…

We construct Riemannian manifolds with singular continuous spectrum embedded in the absolutely continuous spectrum of the Laplacian. Our manifolds are asymptotically hyperbolic with sharp curvature bounds.