arXiv research

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

Study on curvature invariants near singularities of wavefronts.

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.

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.

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 …

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 …

We prove a regularity result for Monge-Ampère equations degenerate along smooth divisor on Kaehler manifolds in Donaldson's spaces of $β$-weighted functions. We apply this result to study the curvature of Kaehler metrics with conical singularities along divisors and give a geometric sufficient condition on the divisor …

We prove a Lorentzian splitting theorem with weakened curvature conditions.

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.

The paper studies degenerations of rational maps and their limits as geometrically finite rational maps.

Method solves optimisation problems on non-Riemannian surfaces with bilateral curvature bounds.

Proves new inequality linking spectral numbers of Lagrangians and their reductions.

We study singularities of Gauss maps of fronts and give characterizations of types of singularities of Gauss maps by geometric properties of fronts which are related to behavior of bounded principal curvatures. Moreover, we investigate relation between a kind of boundedness of Gaussian curvatures near cuspidal edges an…

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

This paper generalizes a result about bounded differentials to higher-order differentials and studies their geometric implications.

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.

Demailly's conjecture, which is a consequence of the Green-Griffiths-Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to provide evidence for Demailly's conjecture by verifying several predictions it makes. We first defi…

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.

Constructs a moduli space for PDEs, linking stability to geometric metrics.

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.

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 $p \in (1,2]$ …

Asymptotically harmonic manifolds are simply connected complete Riemannian manifolds without conjugate points such that all horospheres have the same constant mean curvature $h$. In this article we present results for harmonic functions on rank one asymptotically harmonic manifolds $X$ with mild curvature boundedness c…

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

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…

We prove that if a compact smooth polarized complex manifold admits in the corresponding Hodge Kähler class a conformally Kähler, Einstein--Maxwell metric, or more generally, a Kähler metric of constant $(ξ, a, p)$-scalar curvature, then this metric minimizes the $(ξ,a,p)$-Mabuchi functional. Our method of proof extend…

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

Study proves spacelike self-shrinkers are hyperplanes under certain conditions.

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…