Related papers: Reconstruction Theorem for Germs of Distributions …

This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces…

In a recent landmark paper, Khoa L\^e (2020) established a stochastic sewing lemma which since has found many applications in stochastic analysis. He further conjectured that a similar result may hold in the context of the reconstruction…

Let $M$ be a smooth surface in $\mathbb R^3$ (or a complex surface in $\mathbb C^3$) and $k\geq 2$ be an integer. At any point on $M$ and for any plane in $\mathbb R^3$, we construct a holomorphic map-germ $(\mathbb C^2,0)\to(\mathbb…

Recently, we developed a theory of a geometrically growing system. Here we show that the theory can explain some phenomena of power-law distribution including classical demographic and economic and novel pandemic instances, without…

We give a concise overview of the theory of regularity structures as first exposed in [Hai14]. In order to allow to focus on the conceptual aspects of the theory, many proofs are omitted and statements are simplified. In order to provide…

This paper introduces a novel method for the efficient second-order accurate computation of normal fields from volume fractions on unstructured polyhedral meshes. Locally, i.e. in each mesh cell, an averaged normal is reconstructed by…

We study arithmetic distribution relations and the inverse function theorem in algebraic and arithmetic geometry, with an emphasis on versions that can be applied uniformly across families of varieties and maps. In particular, we prove two…

In the previous paper, the structure of the cut locus was determined for a class of surfaces of revolution homeomorphic to a cylinder. In this paper, we prove the structure theorem of the cut locus for a wider class of surfaces of…

In this monograph, we give an account of the relationship between the algebraic structure of finitely generated and countable groups and the regularity with which they act on manifolds. We concentrate on the case of one--dimensional…

We establish Gromov's celebrated reconstruction theorem in Lorentzian geometry. Alongside this result, we introduce and study a natural concept of isomorphy of normalized bounded Lorentzian metric measure spaces. We outline applications to…

We introduce a (bi)category $\mathfrak{Sing}$ whose objects can be functorially assigned spaces of distributions and generalized functions. In addition, these spaces of distributions and generalized functions possess intrinsic notions of…

We investigate regularizations of distributional sections of vector bundles by means of nets of smooth sections that preserve the main regularity properties of the original distributions (singular support, wavefront set, Sobolev…

The existence of universal unfoldings of certain germs of meromorphic connections is established. This is used to prove a general construction theorem for Frobenius manifolds. A particular case is Dubrovin's theorem on semisimple Frobenius…

Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…

We aim at explaining the most basic ideas underlying two fundamental results in the regularity theory of area minimizing oriented surfaces: De Giorgi's celebrated $\varepsilon$-regularity theorem and Almgren's center manifold. Both theorems…

The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.

This is an expositiry article on collapsing theory in Riemannian geometry written for the Modern Encyclopedia of Mathematical Physics (MEMPhys). We focus on describing the geometric and topological structure of collapsed/non-collapsed…

We present a geometric proof of the averaging theorem for perturbed dynamical systems on a Riemannian manifold, in the case where the flow of the unperturbed vector field is periodic and the $\mathbb{S}^{1}$-action associated to this vector…

We propose an extension of a result by Repetowicz et al. about Wick's theorem and its applications: we first show that Wick's theorem can be extended to the uniform distribution on the sphere and then to the whole class of elliptical…

We develop a regularity and compactness theory for stable capillary minimal hypersurfaces in the half-space $\mathbb{H}^{n+1}$ with contact angle $\theta \in (0,\pi)$ and dimension $n \geq 2$. As a consequence, we obtain the generalized…