Graphs with constant mean curvature in the 3hyperbolic space
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| Format: | Artículo científico |
| Langue: | en |
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Academia Brasileira de Ciências
2002
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| _version_ | 1876466642460868608 |
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| author | Pedro A. Hinojosa |
| author_facet | Pedro A. Hinojosa |
| contents | Graphs with constant mean curvature in the 3hyperbolic space Pedro A. Hinojosa Multidisciplinaria (Ciencias Naturales y Exactas) hyperbolic space constant mean curvature geodesic and horizontal graphs elliptic partial differential equations In thiswork we will deal with disc type surfaces of constant mean curvature in the three dimensionalhyperbolic space which are given as graphs of smooth functions over planar domains. From thevarious types of graphs that could be defined in the hyperbolic space we consider in particularthe horizontal and the geodesic graphs. We proved that if the mean curvature is constant, thensuch graphs are equivalent in the following sense: suppose that M is a constant mean curvaturesurface in the 3-hyperbolic space such that M is a geodesic graph of a function ρ that is zero atthe boundary, then there exist a smooth function f, that also vanishes at the boundary, such thatM is a horizontal graph of f. Moreover, the reciprocal is also true. 2002 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32774301 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.74 |
| format | Artículo científico |
| id | redalyc_32774301 |
| institution | Redalyc |
| language | en |
| publishDate | 2002 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | Graphs with constant mean curvature in the 3hyperbolic space Pedro A. Hinojosa Multidisciplinaria (Ciencias Naturales y Exactas) hyperbolic space constant mean curvature geodesic and horizontal graphs elliptic partial differential equations Graphs with constant mean curvature in the 3hyperbolic space Pedro A. Hinojosa Multidisciplinaria (Ciencias Naturales y Exactas) hyperbolic space constant mean curvature geodesic and horizontal graphs elliptic partial differential equations In thiswork we will deal with disc type surfaces of constant mean curvature in the three dimensionalhyperbolic space which are given as graphs of smooth functions over planar domains. From thevarious types of graphs that could be defined in the hyperbolic space we consider in particularthe horizontal and the geodesic graphs. We proved that if the mean curvature is constant, thensuch graphs are equivalent in the following sense: suppose that M is a constant mean curvaturesurface in the 3-hyperbolic space such that M is a geodesic graph of a function ρ that is zero atthe boundary, then there exist a smooth function f, that also vanishes at the boundary, such thatM is a horizontal graph of f. Moreover, the reciprocal is also true. 2002 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32774301 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.74 |
| title | Graphs with constant mean curvature in the 3hyperbolic space |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) hyperbolic space constant mean curvature geodesic and horizontal graphs elliptic partial differential equations |
| url | https://www.redalyc.org/articulo.oa?id=32774301 |