Search results for "geometry."

Lipschitz Carnot-Carathéodory Structures and their Limits

2022

AbstractIn this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under a mild controllability assumption on the limit vector-fields structure, the distances associated to equi-Lipschitz vector-fields structures that converge uniformly on compact subsets, and to norms that converge uniformly on compact subsets, converge locally uniformly to the limit Carnot-Carathéodory distance. In the case in which the limit distance is boundedly compact, we show that the convergence of the distances is uniform on compact sets. We show an example in which the limit distance is not…

Semigenerated Carnot algebras and applications to sub-Riemannian perimeter

2021

This paper contributes to the study of sets of finite intrinsic perimeter in Carnot groups. Our intent is to characterize in which groups the only sets with constant intrinsic normal are the vertical half-spaces. Our viewpoint is algebraic: such a phenomenon happens if and only if the semigroup generated by each horizontal half-space is a vertical half-space. We call semigenerated those Carnot groups with this property. For Carnot groups of nilpotency step 3 we provide a complete characterization of semigeneration in terms of whether such groups do not have any Engel-type quotients. Engel-type groups, which are introduced here, are the minimal (in terms of quotients) counterexamples. In add…

Topics in the geometry of non-Riemannian lie groups

2017

On osculation, superosculation and characteristic points. Addenda: Computations

1943

Par n dimensiju Eiklīda telpas līknēm

1936

On osculation, superosculation and characteristic points

1943

Translated into English by D. Zeps Original text: Par oskulāciju, superoskulāciju un charakteristiskiem punktiem, https://dspace.lu.lv/dspace/handle/7/46435 Facsimile of the manuscript of dissertation: https://dspace.lu.lv/dspace/handle/7/46446 Facsimile of the manuscript of computations: https://dspace.lu.lv/dspace/handle/7/46433 Page numbers in translation are from original in Latvian

Par oskulāciju, superoskulāciju un charakteristiskiem punktiem. Disertācijas manuskripta faksimils

1943

On Grinbergs' differential geometry and finite fields

2019

Emanuels Grinbergs, in his youth, during ten years, from 1933 until 1943, wrote three dissertations on one subject, namely, differential geometry [1, 2, 3]. We think that his work in this direction has been neglected for many years, and it is the last time to try to understand the significance of these works. Here, in this short article we touch only one aspect of this work, and compare and put together two approaches, one from thesis of Grinbergs [3], and another, of the author's, [5, 6], where we show close relation between both.

Daži pētījumi par telpas ruletēm

1933

Darbs kvalificēts kā Kandidāta darbs, Konkursa darbs, iesniegts LŪ, Matēmatikas nodaļai 1933. g. 14. augustā. Stud. math. Emanuels Grünbergs, Matr. 14875. Motto "Patientia vincet." Disertācijā 143 lpp. Publicējam bez pilnā teksta arī disertācijas ievadu.

Decentralized Deployment of Mobile Sensors for Optimal Connected Sensing Coverage

2008

In this paper, we address the optimal connected sensing coverage problem, i.e., how mobile sensors with limited sensing capabilities can cooperatively adjust their locations so as to maximize the extension of the covered area while avoiding any internal “holes”, areas that are not covered by any sensor. Our solution consists in a distributed motion algorithm that is based on an original extension of the Voronoi tessellation.