Flexible domains for minimal surfaces in Euclidean spaces

Barbara Drinovec-Drnovšek (Author), Franc Forstnerič (Author)

Abstract

V članku uvedemo in raziskujemo nov pojem fleksibilnosti za domene v evklidskih prostorih glede na minimalne ploskve. Domena ▫$\Omega$▫ v ▫$\mathbb{R}^n$▫ se imenuje fleksibilna, če lahko vsako konformno minimalno imerzijo neke Rungejeve domene ▫$U$▫ v odprti Riemannovi ploskvi ▫$M$▫ aproksimiramo enakomerno na kompaktih v ▫$U$▫ s konformnimi minimalnimi imerzijami ▫$M \to \Omega$▫. Skupaj s pojmom hiperboličnosti za minimalne ploskve, obravnavanim v nedavnih delih avtorjev, je dihotomija med fleksibilnostjo in rigidnostjo s tem razširjena iz kompleksne analize v teorijo minimalnih ploskev.

Keywords

minimalna ploskev;fleksibilna domena;hiperbolična domena;Oka mnogoterost;minimal surface;flexible domain;hyperbolic domain;Oka manifold;

Data

Language:	English
Year of publishing:	2023
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.55:514.7
COBISS:	120880899
ISSN:	0022-247X
Views:	235
Downloads:	55
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Fleksibilne domene za minimalne ploskve v evklidskih prostorih
Secondary abstract:	In this paper we introduce and investigate a new notion of flexibility for domains in Euclidean spaces ▫$\mathbb{R}^n$▫ for ▫$n\ge 3$▫ in terms of minimal surfaces which they contain. A domain ▫$\Omega$▫ in ▫$\mathbb{R}^n$▫ is said to be flexible if every conformal minimal immersion ▫$U \to \Omega$▫ from a Runge domain ▫$U$▫ in an open conformal surface ▫$M$▫ can be approximated uniformly on compacts, with interpolation on any given finite set, by conformal minimal immersion ▫$M \to \Omega$▫. Together with hyperbolicity phenomena considered in recent works, this extends the dichotomy between flexibility and rigidity from complex analysis to minimal surface theory.
Secondary keywords:	minimalna ploskev;fleksibilna domena;hiperbolična domena;Okova mnogoterost;
Type (COBISS):	Article
Pages:	art. 126653 (15 str.)
Volume:	ǂVol. ǂ517
Issue:	ǂiss. ǂ2
Chronology:	Jan. 2023
DOI:	10.1016/j.jmaa.2022.126653
ID:	16439149