arXiv research

Embeds LCK manifolds with potential into Hopf manifolds using Riesz-Schauder theorem.

Study centers of convex polyhedrons that are independent of parameters.

The goal of this article is twofold: in a first part, we prove Gaussian estimates for the heat kernel of Schr{ö}dinger operators delta + V whose potential V is "small at infinity" in an integral sense. In a second part, we prove sharp boundedness result for the associated Riesz transform with potential d(delta+V) --1/2…

Study on minimal energy problems for Riesz kernels on manifolds.

In this paper we study the problem of deriving further Sobolev inequalities from a given Sobolev inequality. We use several different methods, including Bessel potentials and Riesz transforms. We apply the results to the Ricci flow to extend the author's results on the $W^{1,2}$ Sobolev inequality along the Ricci flow …

Study on smooth solutions of a nonlinear sigma model with gravitino fields.

Let $(M^\circ, g)$ be an asymptotically conic manifold, in the sense that $M^\circ$ compactifies to a manifold with boundary $M$ in such a way that $g$ becomes a scattering metric on $M$. A special case of particular interest is that of asymptotically Euclidean manifolds, where $\partial M = S^{n-1}$ and the induced me…

We generalize the Riesz potential of a compact domain in $\mathbb{R}^{m}$ by introducing a renormalization of the $r^{α-m}$-potential for $α\le0$. This can be considered as generalization of the dual mixed volumes of convex bodies as introduced by Lutwak. We then study the points where the extreme values of the (renorm…

Paper studies Riesz transform stability under metric perturbations.

Uniform boundedness of Riesz transforms on Riemannian manifolds is established with a dichotomy.

Riesz regression connects to density ratio estimation for causal inference.

We investigate the boundness of the Riesz transform on $L^p$ for connected sum of manifolds where the Riesz transform is bounded on $L^p$.

Unified framework for debiased machine learning using Riesz representer and Bregman divergence.

There is an interesting potential theory associated to each degenerate elliptic, fully nonlinear equation $f(D^2u) = 0$. These include all the potential theories attached to calibrated geometries. This paper begins the study of tangents to the subsolutions in these theories, a topic inspired by the results of Kiselman …

Study proves NN matching is equivalent to Riesz regression for debiased machine learning.

New manifolds show Riesz transform unbounded for p > 2.

New conditions found for uniqueness of a center in Rm.

Develops a direct debiased machine learning framework using Bregman divergence.

Gradient boosting estimates Riesz representer for causal inference.

Unified theory for causal inference using various methods.

We show a perturbation result for the boundedness of the Riesz transform : if $M$ and $M_0$ are complete Riemannian manifolds satisfying a Sobolev inequality of dimension $n$, which are isometric outside a compact set, and if the Riesz transform on $M_0$ is bounded on $L^q$, then for all $\frac{n}{n-2}, the Riesz trans…

Python package automates causal parameter estimation using Riesz regression.

Balls, circles, and spheres identified by energy of distances.

In this paper we prove mixed norm estimates for Riesz transforms related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. These operators are closely related to the Riesz transforms for Jacobi polynomials expansions. The key point is to obtain sharp estimates for the kernel of the Jaco…

We investigate the $L^p$-boundness of the Riesz transform on Riemannian manifolds whose Ricci curvature has quadratic decay. Two criteria for the $L^p$-unboundness of the Riesz transform are given. We recover known results about manifolds that are Euclidean or conical at infinity.

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

Two approaches to directly estimating Riesz representer are shown to be numerically equivalent under certain conditions.

For nearly spherical bodies, the unique center is proven under certain conditions.

New Riesz distributions for differential forms on Euclidean space.

New function found with spherical harmonic divergent sums almost everywhere.

The study bounds Riesz transforms on manifolds with controlled curvature.

Two regularization methods show similar results for Riesz energies of submanifolds.

Estimates heat kernel gradients on fractal-like cable systems.

Estimates for covariant derivatives and Riesz transforms on differential forms.

Extends potential theory to Carnot groups, estimating Hausdorff dimension.

Unified framework for estimating density ratios in causal inference.

Graph continuous operators become Riesz continuous after multiplication by unitary operators.

Proposes adversarial method to estimate Riesz representer.

We analyze the resolvent $R(k)=(P+k^2)^{-1}$ of Schrödinger operators $P=Δ+V$ with short range potential $V$ on asymptotically conic manifolds $(M,g)$ (this setting includes asymptotically Euclidean manifolds) near $k=0$. We make the assumption that the dimension is greater or equal to 3 and that $P$ has no $L^2$ null …

We study the validity of the $L^p$ inequality for the Riesz transform when $p>2$ and of its reverse inequality when $p<2$ on complete Riemannian manifolds under the doubling property and some Poincaré inequalities.

In this paper we study the Riesz transform on complete and connected Riemannian manifolds $M$ with a certain spectral gap in the $L^2$ spectrum of the Laplacian. We show that on such manifolds the Riesz transform is $L^p$ bounded for all $p \in (1,\infty)$. This generalizes a result by Mandouvalos and Marias and extend…

We give new estimates for a critical elliptic system introduced by Rivière-Struwe in \cite{riviere_struwe} (see also the work of Rupflin \cite{rupflin} and Schikorra \cite{schikorra_frames}), which generalises PDE solved by harmonic (and almost harmonic) maps from a Euclidean ball $B_1 \In \R^n$ into Riemannian manifol…

ScoreMatchingRiesz improves debiased machine learning and policy effects estimation.

Researchers study Riesz transforms on complex groups, proving boundedness results.

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

We prove an optimal reverse Poincaré inequality for the heat semigroup generated by the sub-Laplacian on a Carnot group of any step. As an application we give new proofs of the isoperimetric inequality and of the boundedness of the Riesz transform in Carnot groups.

Improved AutoDML estimator for causal inference using outcome-adapted shared covariate representation.

Let $M$ be a smooth Riemannian manifold which is the union of a compact part and a finite number of Euclidean ends, $\RR^n \setminus B(0,R)$ for some $R > 0$, each of which carries the standard metric. Our main result is that the Riesz transform on $M$ is bounded from $L^p(M) \to L^p(M; T^*M)$ for $1 < p < n$ and unbou…