Year: 2026
Type: preprint
Abstract: We study disjoint solution pairs $(u,D)$ to the minimal surface equation in $\mathbb{R}^n$, with $u=0$ on $\partial D.$ A conjecture of W. Meeks states that at most two such pairs can exist in $\mathbb{R}^n.$ We confirm the conjecture in two complementary cases. For $n\in\{2,3,4,5,6\},$ we prove it under a superlinearity assumption. In dimension $n=2,$ we establish the result under a suitable sublinearity assumption. We also derive estimates on the asymptotic angle of domains supporting nontrivial solutions for $n\geq 3.$
Source: arXiv (Cornell University)
Authors: Benedetti, Angelo, Nelli, Barbara
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G810296040
OpenAlex ID: W7222252675