scholarly journals A Note on Minimal Translation Graphs in Euclidean Space

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 889 ◽  
Author(s):  
Dan Yang ◽  
Jingjing Zhang ◽  
Yu Fu
Keyword(s):  
Euclidean Space ◽  
Translation Surfaces ◽  
Planar Curves

In this note, we give a characterization of a class of minimal translation graphs generated by planar curves. Precisely, we prove that a hypersurface that can be written as the sum of n planar curves is either a hyperplane or a cylinder on the generalized Scherk surface. This result can be considered as a generalization of the results on minimal translation hypersurfaces due to Dillen–Verstraelen–Zafindratafa in 1991 and minimal translation surfaces due to Liu–Yu in 2013.

On Vitali's Theorem for Groups of Motions of Euclidean Space

1999 ◽  
Vol 6 (4) ◽  
pp. 323-334
Author(s):  
A. Kharazishvili
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Finite Dimensional

Abstract We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem [Sul problema della misura dei gruppi di punti di una retta, 1905] holds true. This characterization is formulated in purely geometrical terms.

Harmonic curvatures of the strip in Minkowski space

2018 ◽  
Vol 11 (04) ◽  
pp. 1850061
Author(s):  
Filiz Ertem Kaya ◽  
Ayşe Yavuz
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Strip Theory ◽  
First Time ◽  
Cylindrical Helix

This study aimed to give definitions and relations between strip theory and harmonic curvatures of the strip in Minkowski space. Previously, the same was done in Euclidean Space (see [F. Ertem Kaya, Y. Yayli and H. H. Hacısalihoglu, A characterization of cylindrical helix strip, Commun. Fac. Sci. Univ. Ank. Ser. A1 59(2) (2010) 37–51]). The present paper gives for the first time a generic characterization of the harmonic curvatures of the strip, helix strip and inclined strip in Minkowski space.

MAXIMAL COMPUTABILITY STRUCTURES

2016 ◽  
Vol 22 (4) ◽  
pp. 445-468 ◽  
Author(s):  
ZVONKO ILJAZOVIĆ ◽  
LUCIJA VALIDŽIĆ
Keyword(s):  
Euclidean Space ◽  
Metric Space ◽  
Dense Sequence

AbstractA computability structure on a metric space is a set of sequences which satisfy certain conditions. Of a particular interest are those computability structures which contain a dense sequence, so called separable computability structures. In this paper we observe maximal computability structures which are more general than separable computability structures and we examine their properties. In particular, we examine maximal computability structures on subspaces of Euclidean space, we give their characterization and we investigate conditions under which a maximal computability structure on such a space is unique. We also give a characterization of separable computability structures on a segment.

scholarly journals On spatial matchings: The first-in-first-match case

2021 ◽  
Vol 53 (3) ◽  
pp. 757-800
Author(s):  
Mayank Manjrekar
Keyword(s):  
Steady State ◽  
Euclidean Space ◽  
Compact Space ◽  
Arrival Time ◽  
Type Inequality ◽  
Stationary Regime ◽  
Constant Rate ◽  
The One ◽  
Opposite Color

AbstractWe describe a process where two types of particles, marked red and blue, arrive in a domain at a constant rate. When a new particle arrives into the domain, if there are particles of the opposite color present within a distance of 1 from the new particle, then, among these particles, it matches to the one with the earliest arrival time, and both particles are removed. Otherwise, the particle is simply added to the system. Additionally, particles may lose patience and depart at a constant rate. We study the existence of a stationary regime for this process, when the domain is either a compact space or a Euclidean space. In the compact setting, we give a product-form characterization of the stationary distribution, and then prove an FKG-type inequality that establishes certain clustering properties of the particles in the steady state.

scholarly journals Distance functions and umbilic submanifolds of hyperbolic space

1979 ◽  
Vol 74 ◽  
pp. 67-75 ◽  
Author(s):  
Thomas E. Cecil ◽  
Patrick J. Ryan
Keyword(s):  
Riemannian Manifold ◽  
Euclidean Space ◽  
Hyperbolic Space ◽  
Critical Points ◽  
Morse Function ◽  
Complete Riemannian Manifold ◽  
Distance Functions

In 1972, Nomizu and Rodriguez [5] found the following characterization of the complete umbilic submanifolds of Euclidean space.Theorem A. Let Mn, n ≥ 2, be a connected, complete Riemannian manifold isometrically immersed in a Euclidean space Em. Every Morse function of the form Lp has index 0 or n at all of its critical points if and only if Mnis embedded as a Euclidean n-subspace or a Euclidean n-sphere in Em.

Minimal Translation Surfaces in Euclidean Space

2017 ◽  
Vol 27 (4) ◽  
pp. 2926-2937 ◽  
Author(s):  
Rafael López ◽  
Óscar Perdomo
Keyword(s):  
Euclidean Space ◽  
Translation Surfaces ◽  
Surfaces In Euclidean Space
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