scholarly journals Local $C^{1,\beta }$-regularity at the boundary of two dimensional sliding almost minimal sets in $\mathbb {R}^{3}$

2021 ◽  
Vol 8 (5) ◽  
pp. 130-189
Author(s):  
Yangqin Fang
Keyword(s):  
Two Dimensional ◽  
Minimal Sets

Proper minimal sets on compact connected 2-manifolds are nowhere dense

2008 ◽  
Vol 28 (3) ◽  
pp. 863-876 ◽  
Author(s):  
SERGII˘ KOLYADA ◽  
L’UBOMÍR SNOHA ◽  
SERGEI˘ TROFIMCHUK
Keyword(s):  
Dynamical System ◽  
Recent Result ◽  
Dense Subset ◽  
Klein Bottle ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Minimal Set ◽  
Minimal Sets ◽  
Continuous Map

AbstractLet $\mathcal {M}^2$ be a compact connected two-dimensional manifold, with or without boundary, and let $f:{\mathcal {M}}^2\to \mathcal {M}^2$ be a continuous map. We prove that if $M \subseteq \mathcal {M}^2$ is a minimal set of the dynamical system $(\mathcal {M}^2,f)$ then either $M = \mathcal {M}^2$ or M is a nowhere dense subset of $\mathcal {M}^2$. Moreover, we add a shorter proof of the recent result of Blokh, Oversteegen and Tymchatyn, that in the former case $\mathcal {M}^2$ is a torus or a Klein bottle.

Minimal Sets of Antitriangular Maps

2003 ◽  
Vol 13 (07) ◽  
pp. 1733-1741 ◽  
Author(s):  
F. Balibrea ◽  
A. Linero ◽  
J. S. Canovas
Keyword(s):  
Two Dimensional ◽  
Interval Maps ◽  
Minimal Sets ◽  
Infinite Case

We consider the class of two-dimensional maps of the form F(x,y) = (g(y),f(x)), (x,y) ∈ [0,1] × [0,1] = I2, where f and g are continuous interval maps. The paper deals with the structure of minimal sets for this class of maps. We give a complete description of finite minimal sets and prove some partial results concerning the infinite case.

scholarly journals Hölder regularity at the boundary of two-dimensional sliding almost minimal sets

2018 ◽  
Vol 11 (1) ◽  
pp. 29-63
Author(s):  
Yangqin Fang
Keyword(s):  
Regularity Result ◽  
Hölder Regularity ◽  
Two Dimensional ◽  
Soap Films ◽  
Regularity Theorem ◽  
Plateau’S Problem ◽  
Minimal Sets ◽  
Plateau's Problem ◽  
Dimension 2 ◽  
Holder Regularity

AbstractIn [15], Jean Taylor proved a regularity theorem away from the boundary for Almgren almost minimal sets of dimension 2 in {\mathbb{R}^{3}}. It is quite important for understanding the soap films and the solutions of Plateau’s problem away from boundary. In this paper, we will give a regularity result on the boundary for two-dimensional sliding almost minimal sets in {\mathbb{R}^{3}}.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

Sign in / Sign up

Export Citation Format

Share Document