20.500.12556/DiRROS-18651 Domains without parabolic minimal submanifolds and weakly hyperbolic domains 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. minimal surfaces m-plurisubharmonic functions hyperbolic domain minimalne ploskve ▫$m$▫-plurisubharmonične funkcije hiperbolična domena true false true Angleški jezik Slovenski jezik Neznano 2024-04-10 09:31:24 2024-04-10 09:31:24 2024-04-11 03:34:32 0000-00-00 00:00:00 2023 0 0 str. 2778-2792 iss. 6 Vol. 55 Dec. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-12-01 517.5 0024-6093 10.1112/blms.12894 161694467 Bulletin_of_London_Math_Soc_-_2023_-_Forstneric_-_Domains_without_parabolic_minimal_submanifolds_and_weakly_hyperbolic.pdf Bulletin_of_London_Math_Soc_-_2023_-_Forstneric_-_Domains_without_parabolic_minimal_submanifolds_and_weakly_hyperbolic.pdf 1 968AF422A5EFB57D0AF9C573CD9E8476 82716c05a3569208e0ebf0cf8507ed65db51529418d52efc7ff031a89a4f7103 c9eac58b-f6fb-11ee-ae20-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25479 https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.12894 1 92c7cf6e-f6fb-11ee-ae20-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25478 Inštitut za matematiko, fiziko in mehaniko 0 0 0