Article
A Hopf theorem for open surfaces in product spaces
Author/s | Carmo, Manfredo do
Fernández Delgado, Isabel |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2009 |
Deposit Date | 2021-07-06 |
Published in |
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Abstract | Hopf’s theorem has been recently extended to compact genus zero surfaces with
constant
mean curvature H in a product space Mk
2 ×R, whereMk
2 is a surface with constant Gaussian
curvature k = 0 [AbRo]. It also has ... Hopf’s theorem has been recently extended to compact genus zero surfaces with constant mean curvature H in a product space Mk 2 ×R, whereMk 2 is a surface with constant Gaussian curvature k = 0 [AbRo]. It also has been observed that, rather than H = const., it suffices to assume that the differential dH of H is appropriately bounded [AdCT]. Here, we consider the case of simply-connected open surfaces with boundary in Mk 2 ×R such that dH is appropriately bounded and certain conditions on the boundary are satisfied, and show that such surfaces can all be described. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Project ID. | MTM2004-00160 |
Citation | Carmo, M.d. y Fernández Delgado, I. (2009). A Hopf theorem for open surfaces in product spaces. Forum Mathematicum, 21 (6), 951-963. |
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