Related papers: Dendritations of Surfaces
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
This is a book on derived foliations, that are a generalisation of classical foliations in the context of derived geometry. The text starts with the basic definitions and constructions, then explore foliated cohomology (with crystal…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and…
The theory of geometric structures on a surface with nonempty boundary can be developed by using a decomposition of such a surface into hexagons, in the same way as the theory of geometric structures on a surface without boundary is…
A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures. The thesis…
We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.
We study the moduli space of euclidean structures with cone points on a surface, and describe a decomposition into cells each of which corresponds to a given combinatorial type of Delaunay tessellation. We use some of the ideas to study…
Decompositions on manifolds appear in various geometric structures. Necessary and sufficient conditions for quotient spaces of decompositions to be manifolds are widely characterized. We characterize necessary and sufficient conditions to…
In this article, we show that for any deformation of analytic foliations, there exists a maximal analytic singular foliation on the space of parameters along the leaves of which the deformation is integrable.
We survey the distributional properties of progressively dilating sets under projection by covering maps, focusing on manifolds of constant sectional curvature. In the Euclidean case, we review previously known results and formulate some…
In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the…
We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying…
We study the space of deformations of a smooth foliation of the 5-sphere by complex manifolds
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.
In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In the last decade, several of these have been constructed,…
Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…