arXiv research

The paper studies boundedness of pseudo-differential operators on smooth manifolds.

Study proves boundedness of operators in variable exponent Morrey spaces.

Study examines $L^p$-boundedness of Hodge projection on manifolds with ends.

The study shows boundedness and constructs a moduli space for Calabi-Yau fibrations.

Characterizes Schrödinger operator boundedness on weighted Riemannian manifolds.

Study examines boundedness of oscillating singular integrals on specific Lie groups.

This paper proves geodesic curvature measures are bounded for curves near cross cap singularities.

Paper refines Chen-Cheng's estimates for Kähler metrics.

Paper presents a novel method to assess boundedness and stability of nonlinear systems with variable delays.

Study on flat connections with controlled irregularity.

Study confirms boundedness of certain singularities in log Fano geometry.

We establish a general "boundedness implies convergence" principle for a family of evolving Riemannian metrics. We then apply this principle to collapsing Calabi-Yau metrics and normalized Kähler-Ricci flows on torus fibered minimal models to obtain convergence results.

Paper characterizes foliated bundle classes via quasi-morphisms and studies their boundedness.

The paper proves boundedness of a Riesz transform on weighted manifolds.

Let $M$ be a complete non-compact Riemannian manifold. In this paper, we derive sufficient conditions on metric perturbation for stability of $L^p$-boundedness of the Riesz transform, $p\in (2,\infty)$. We also provide counter-examples regarding in-stability for $L^p$-boundedness of Riesz transform.

We prove that a Ricci flow cannot develop a finite time singularity assuming the boundedness of a suitable space-time integral norm of the curvature tensor. Moreover, the extensibility of the flow is proved under a Ricci lower bound and the boundedness of a space-time integral norm of the scalar curvature.

We give a characterization of relative Ding stable toric Fano manifolds in terms of the behavior of the modified Ding functional. We call the corresponding behavior of the modified Ding functional the pseudo-boundedness from below. We also discuss the pseudo-boundedness of the Ding / Mabuchi functional of general Fano …

The study shows boundedness of certain fibered varieties in algebraic geometry.

Study $L^p$ boundedness of Riesz transform on differential forms for certain manifolds.

The paper examines geometric invariants near a specific type of singular point.

Let $G = N \rtimes A$, where $N$ is a stratified group and $A = \mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous sub-Laplacians on $N$ and $A$ can be lifted to left-invariant operators on $G$ and their sum is a sub-Laplacian $Δ$ on $G$. Here we prove weak type $(1,1)$, $L^p$-boundedness for $p \in (1,2]$ …

Local positive definite Z2^n-superfunctions can be extended.

Study on curvature invariants near singularities of wavefronts.

The paper examines the boundedness of bundle diffeomorphism groups over a circle.

The paper examines boundedness of diffeomorphism groups of manifold pairs, focusing on the circle case.

We prove boundedness and polynomial decay statements for solutions to the spin $\pm1$ Teukolsky-type equation projected to the $\ell=1$ spherical harmonic on Reissner-Nordström spacetime. The equation is verified by a gauge-invariant quantity which we identify and which involves the electromagnetic and curvature tensor…

Proves boundedness of log Fano cone singularities with bounded local volumes.

We consider Kerr spacetimes with parameters a and M such that |a|<< M, Kerr-Newman spacetimes with parameters |Q|<< M, |a|<< M, and more generally, stationary axisymmetric black hole exterior spacetimes which are sufficiently close to a Schwarzschild metric with parameter M>0, with appropriate geometric assumptions on …

The paper proves boundedness and decay of Teukolsky equations on Kerr backgrounds.

Upper bound on expected supremum of Bernoulli process.

New stability framework relaxes boundedness assumptions for generalization bounds.

Paper proves convergence of SA algorithm via martingale and converse Lyapunov methods.

This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A non-standard stochastic differential equation, with neither Lipschitz continuity n…

This note relaxes conditions for Kähler metrics with bounded entropy and scalar curvature.

The paper analyzes Teukolsky equations on Kerr backgrounds, proving boundedness and decay of solutions.

It is shown that certain diffeomorphism or homeomorphism groups with no restriction on support of an open manifold with finite number of ends are bounded. It follows that these groups are uniformly perfect. In order to characterize the boundedness several conditions on automorphism groups of an open manifold are introd…

We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and in high probability. For any (possibly non-convex) class, the excess loss of a …

The J-flow is a parabolic flow on Kahler manifolds. It was defined by Donaldson in the setting of moment maps and by Chen as the gradient flow of the J-functional appearing in his formula for the Mabuchi energy. It is shown here that under a certain condition on the initial data, the J-flow converges to a critical metr…

Paper reinterprets majorizing measure theorem in terms of coding theory.

Global existence and boundedness proved for quasilinear wave equations on Kerr black holes.

The paper estimates curvature for a specific flow on manifolds.

Paper shows robustness of kernel-based pairwise learning without strict assumptions.

We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.

A group is said to be bounded if it has a finite diameter with respect to any bi-invariant metric. In the present paper we discuss boundedness of various groups of diffeomorphisms.

We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restrict ourselves to the normalized Laplacian and, more generally, we do not impose any boundedness assumption on the geometry. This is achieved …

Study shows boundedness of klt singularities in 3D or with bounded Kollár components.

This paper establishes geometric obstructions to the existence of complete, properly embedded, mean curvature flow self-translating solitons $Σ^n\subseteq \mathbb{R}^{n+1}$, generalizing previously known non-existence conditions such as cylindrical boundedness.

Although ADAM is a very popular algorithm for optimizing the weights of neural networks, it has been recently shown that it can diverge even in simple convex optimization examples. Several variants of ADAM have been proposed to circumvent this convergence issue. In this work, we study the ADAM algorithm for smooth nonc…