Related papers: On Differential and Riemannian Calculus on Wassers…

We consider the topological and geometric reconstruction of a geodesic subspace of $\mathbb{R}^N$ both from the \v{C}ech and Vietoris-Rips filtrations on a finite, Hausdorff-close, Euclidean sample. Our reconstruction technique leverages…

It is shown that any open Riemann surface can be immersed in any Stein manifold with (volume) density property and of dimension at least 2, if the manifold possesses an exhaustion with holomorphically convex compacts such that their…

We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We show that without any curvature assumption, the smoothness of…

Very recently, Bai [Linear Algebra Appl., 681:150-186, 2024 \& Appl. Math. Lett., 166:109510, 2025] studied some concrete structures, and obtained essential algebraic and computational properties of the one-dimensional, two-dimensional and…

Let G be a compact connected Lie group which is equipped with a bi-invariant Riemannian metric. Let m(x,y)=xy be the multiplication operator. We show the associated fibration m mapping GxG to G is a Riemannian submersion with totally…

In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman…

This paper starts by introducing results from geometric measure theory to prove symmetric decreasing rearrangement inequalities on $\mathbb{R}^n$, which give multiple proofs of the isoperimetric and P\'{o}lya-Szeg\H{o} inequalities. Then we…

Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…

Profinite algebras are the residually finite compact algebras; their underlying topological spaces are Stone spaces. We extend the theory of profinite algebras to a more general setting of Stone topological algebras. We introduce Stone…

We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of a multi-linear algebraic structure on the space of smooth functions. In particular, we find algebraic expressions for…

Let $M$ be an even-dimensional, oriented closed manifold. We show that the restriction of a singular Riemannian flow on $M$ to a small tubular neighborhood of each connected component of its singular stratum is foliated-diffeomorphic to an…

We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations…

We introduce the notion of a manifold admitting a simple compact Cartan 3-form $\om^3$. We study algebraic types of such manifolds specializing on those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form…

We study a natural Wasserstein gradient flow on manifolds of probability distributions with discrete sample spaces. We derive the Riemannian structure for the probability simplex from the dynamical formulation of the Wasserstein distance on…

The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine…

This paper develops a discrete theory of real Riemann surfaces based on quadrilateral cellular decompositions (quad-graphs) and a linear discretization of the Cauchy-Riemann equations. We construct a discrete analogue of an antiholomorphic…

We integrate in closed implicit form the Navier-Stokes equations for an incompressible fluid and the kinematical dynamo equation, in smooth manifolds and Euclidean space. This integration is carried out by applying Stochastic Differential…

We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the…

In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion…

Certain natural geometric approximation schemes are developed for Wiener measure on a compact Riemannian manifold. These approximations closely mimic the informal path integral formulas used in the physics literature for representing the…