Domains without parabolic minimal submanifolds and weakly hyperbolic domains

Forstnerič, Franc (avtor)

We show that if $\Omega$ is an $m$-convex domain in $\mathbb{R}^n$ for some $2 \le m < n$ whose boundary $b\Omega$ has a tubular neighbourhood of positive radius and is not $m$-flat near infinity, then $\Omega$ does not contain any immersed parabolic minimal submanifolds of dimension $\ge m$. In particular, if $M$ is a properly embedded non-flat minimal hypersurface in $\mathbb{R}^n$ with a tubular neighbourhood of positive radius, then every immersed parabolic hypersurface in $\mathbb{R}^n$ intersects $M$. In dimension $n=3$, this holds if $M$ has bounded Gaussian curvature function. We also introduce the class of weakly hyperbolic domains $\Omega$ in $\mathbb{R}^n$, characterised by the property that every conformal harmonic map $\mathbb{C} \to \Omega$ is constant, and we elucidate their relationship with hyperbolic domains, and domains without parabolic minimal surfaces.

• Jezik: Angleški jezik
• Ključne besede: minimal surfaces, $m$-plurisubharmonic functions, hyperbolic domain
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: Str. 2778-2792
• Številčenje: Vol. 55, iss. 6
• PID: 20.500.12556/RUL-152922
• UDK: 517.5
• ISSN pri članku: 0024-6093
• DOI: 10.1112/blms.12894
• COBISS.SI-ID: 161694467
• Datum objave v RUL: 12.12.2023

Gradivo je del revije

• Naslov: Bulletin of the London Mathematical Society
• Skrajšan naslov: Bull. Lond. Math. Soc.
• Založnik: Wiley, London Mathematical Society
• ISSN: 0024-6093
• COBISS.SI-ID: 25154560

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: minimalne ploskve, $m$-plurisubharmonične funkcije, hiperbolična domena