Abstract
Given Ω ⊂ ℝ3an open bounded set with smooth boundary ∂Ω and H ∈ ℝ, we prove the existence of embedded H-surfaces supported by ∂Ω, that is regular surfaces in ℝ3with constant mean curvature H at every point, contained in Ω and with boundary intersecting ∂Ω orthogonally. More precisely, we prove that if Q ∈ ∂Ω is a stable stationary point for the mean curvature of ∂Ω, then there exists a family of embedded [Formula: see text]-surfaces near Q, ε > 0 small, which, once dilated by a factor [Formula: see text] and suitably translated, converges to a hemisphere of radius 1 as ε → 0.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
