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Let (M,g) be a compact, connected and oriented Riemannian manifold. We denote D the space of smooth probability density functions on M.
Using the language of Alesker's theory of valuations on manifolds, a thorough account of the integral geometry of the complex space forms is given. The local kinematic formulas on complex space forms ...
We show that the Kakimizu complex of minimal genus Seifert surfaces for a knot in the 3-sphere is quasi-isometric to a Euclidean integer lattice $\mathbb Z^n$ for some $n \geq 0$.
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions.
Based on a description of project networks by max-plus algebra and poset, the adjacency of critical paths is presented using tropical geometry.
We study the geometry of point-orbits of elation groups with a given center and axis of a finite projective space. We show that there exists a 1-1 correspondence from conjugacy classes of such groups ...
By applying differential geometry to analogue models developed such a model is calculated for the geometrical shape. Dip measurements are critical data for geologists, and in particular for structural...
Abstract: Cheeger's finiteness theorem bounds the number of diffeomorphism types of manifolds with bounded curvature, diameter and volume; the Hadamard--Cartan theorem, as popularized by Gromov, shows...
Abstract: We consider random systems of linear equations over GF(2) in which every equation binds k variables. We obtain a precise description of the clustering of solutions in such systems. In partic...
Abstract: In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of...
The return to the quiescent state of the Anomalous X-ray pulsar XTE J1810-197 following its 2003 outburst represents a unique opportunity to probe the surface emission properties of a magnetar. The qu...
Abstract: We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After revi...
Abstract: Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand ...
Abstract: This text is devoted to the systematic study of flatness in the context of Berkovich analytic spaces. After having shown through a counter-example that naive flatness in that context is not ...
Abstract: Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group st...

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