相关论文: Quantiles on global non-positive curvature spaces
One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on…
We develop a class of regular black holes by prescribing finite curvature invariants and reconstructing the corresponding spacetime geometry. Two distinct approaches are employed: one based on the Ricci scalar and the other on the Weyl…
By virtue of harmonic maps on two-dimensional spheres (S$^{2}$), a topological quantization in spacetime is proposed. The discrete character of all physical quantities follows naturally. A Schwarzschild black hole, non-black hole and…
Hyperbolic neural networks (HNNs) have demonstrated notable efficacy in representing real-world data with hierarchical structures via exploiting the geometric properties of hyperbolic spaces characterized by negative curvatures. Curvature…
We obtain an explicit formula for comparing total curvature of level sets of functions on Riemannian manifolds, and develop some applications of this result to the isoperimetric problem in spaces of nonpositive curvature.
This paper considers quantile regression for a wide class of time series models including ARMA models with asymmetric GARCH (AGARCH) errors. The classical mean-variance models are reinterpreted as conditional location-scale models so that…
High-dimensional datasets typically cluster around lower-dimensional manifolds but are also often marred by severe noise, obscuring the intrinsic geometry essential for downstream learning tasks. We present a quantum algorithm for…
Building on the recently introduced notion of quantum Ricci curvature and motivated by considerations in nonperturbative quantum gravity, we advocate a new, global observable for curved metric spaces, the curvature profile. It is obtained…
We prove local and global upper estimates for the infimum of the mean curvature, the scalar curvature and the norm of the shape operator of graphs in a warped product space. Using these estimates, we obtain some results on pseudo-hyperbolic…
In this note, we investigate the existence of smooth complete hypersurfaces in hyperbolic space with constant $(n-2)$-curvature and a prescribed asymptotic boundary at infinity. Previously, the existence was known only for a restricted…
We construct a quantization of the moduli space $\mathcal{GH}_\Lambda(S\times\mathbb{R})$ of maximal globally hyperbolic Lorentzian metrics on $S\times \mathbb{R}$ with constant sectional curvature $\Lambda$, for a punctured surface $S$.…
In this paper we show an abundance of complete K\"ahler metrics with negative holomorphic bisectional curvature on total spaces of certain vector bundles. Assume that such total spaces are endowed with a wider class of nonpositively curved…
In this paper, we study functional and geometric inequalities on complete Finsler measure spaces under the condition that the weighted Ricci curvature ${\rm Ric}_\infty$ has a lower bound. We first obtain some local uniform Poincar\'{e}…
We establish local elliptic and parabolic gradient estimates for positive smooth solutions to a nonlinear parabolic equation on a smooth metric measure space. As applications, we determine various conditions on the equation's coefficients…
This article presents new parabolic and elliptic type gradient estimates for positive smooth solutions to a nonlinear parabolic equation involving the Witten Laplacian in the context of smooth metric measure spaces. The metric and potential…
The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence…
The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The $N$-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of…
We find complete hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of (elliptic) curvature functions which includes the higher order mean curvatures and their…
In this paper we continue our study of finding the curvature flow of complete hypersurfaces in hyperbolic space with a prescribed asymptotic boundary at infinity. Our main results are proved by deriving a priori global gradient estimates…