The Prescribed Mean Curvature Problem for Embedding Sphere–A New Existence Theorem of Yau Problem
Year: 2026
Type: article
Abstract: The prescribed mean curvature problem is raised by Yau [16] as the following questions: is there an n-dimensional unit sphere $$X:{\mathbb {S}^{n}(1)}\longrightarrow {\mathbb {R}^{n+1}}$$ X : S n ( 1 ) ⟶ R n + 1 embedded in $$(n+1)$$ ( n + 1 ) -dimensional Euclidean space whose mean curvature is a prescribed function H defined on $${\mathbb {R}^{n+1}}$$ R n + 1 ? Stimulating by Bakelman, Kantor [1], Treibergs and Wei [14], the author established a new existence theorem for this classical problem by observing some new appropriate conditions which are natural and simple.
Source: Journal of Geometric Analysis
Author: Bangchao Yin
Institution: Yunnan Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7164049132