Related papers: Geometry of cuspidal edges with boundary

In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation spaces.

For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…

Neural fields are receiving increased attention as a geometric representation due to their ability to compactly store detailed and smooth shapes and easily undergo topological changes. Compared to classic geometry representations, however,…

We introduce a new isomorphism invariant for generalized Baumslag-Solitar (GBS) groups, which we call the limit angle. Unlike previously known invariants, which are primarily algebraic, the limit angle admits a dynamical interpretation,…

We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.

We study of the shape of a compact singular minimal surface in terms of the geometry of its boundary, asking what type of {\it a priori} information can be obtained on the surface from the knowledge of its boundary. We derive estimates of…

In this note, we discuss the interactions between differential topology and isoparametric foliations, surveying some recent progress and open problems.

To study a one parameter deformation of an $S_1$ singularity taking into consideration its differential geometric properties, we give a form representing the deformation using only diffeomorphisms on the source and isometries of the target.…

The theory of spaces with different (not only by sign) contravariant and covariant affine connections and metrics [}$(\bar{L}_n,g)$\QTR{it}{-spaces] is worked out within the framework of the tensor analysis over differentiable manifolds and…

We study the Picard variety of the Fano surface of nodal and mildly cuspidal cubic threefolds in arbitrary characteristic by relating divisors on the Fano surface to divisors on the symmetric product of a curve of genus 4.

We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M.…

We review several algebraic, combinatorial and geometric interpretations of motivic Donaldson-Thomas invariants of symmetric quivers.

The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…

We study conformal deformation problems on manifolds with boundary which include prescribing $\sigma_k\equiv0$ in the interior. In particular, we prove a Dirichlet principle when the induced metric on the boundary is fixed and an Obata-type…

Geometrical properties of holonomic and non holonomic varieties defined by the Pfaff equations connected with a first order systems of differential equations are studied. The Riemann extensions of affine connected spaces for investigation…

A surface with boundary is randomly generated by gluing polygons along some of their sides. We show that its genus and number of boundary components asymptotically follow a bivariate normal distribution.

Symmetries and the corresponding fields of differential invariants of the inviscid flows on a curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given.

This note presents two observations which have in common that they lie at the boundary of toric geometry. The first one because it concerns the deformation of affine toric varieties into non toric germs in order to understand how to avoid…

We study linearizability of actions of finite groups on cubic threefolds with nonnodal isolated singularities.

Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such…