Related papers: Geometrical embeddings for distributions into alge…

For any n-dimensional compact Riemannian manifold (M,g), we construct a canonical t-family of isometric embeddings I_{t}: M->R^{q(t)}, with t>0 sufficiently small and q(t)>>t^{-n/2}. This is done by intrinsically perturbing the heat kernel…

Using the results of \cite{P1}, we get some estimates of warping functions for isometric immersions by changing the target manifolds by some types of Riemannian manifolds: constant space forms and Hermitian symmetric spaces. And we deal…

For a complete noncompact connected Riemannian manifold with bounded geometry, we prove a compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit…

The paper is devoted to differential geometry of singular distributions (i.e., of varying dimension) on a Riemannian manifold. Such distributions are defined as images of the tangent bundle under smooth endomorphisms. We prove the novel…

We develop some foundations for the theory of formal derived algebraic geometry, which parallel the theory of formal spectral algebraic geometry by Jacob Lurie. For this, we establish a close connection between algebro-geometric objects in…

This work proposes a geometric insight into equivariant message passing on Riemannian manifolds. As previously proposed, numerical features on Riemannian manifolds are represented as coordinate-independent feature fields on the manifold. To…

Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…

We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…

This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic…

We introduce an intrinsic deformation of the algebra of smooth functions on a compact Riemannian manifold using only the Laplace spectral decomposition. The construction twists the canonical multiplication-projection channels by unimodular…

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…

We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.

A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…

The isometric embedding problem is a fundamental problem in differential geometry. A longstanding problem is considered in this paper to characterize intrinsic metrics on a two-dimensional Riemannian manifold which can be realized as…

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.

A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…

A mechanism for the inheritance of properties of spectra by differential spectra is developed and applied to prove geometric properties of morphisms of differential algebraic varieties.

A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.