| 词条 | Bryant surface |
| 释义 |
In Riemannian geometry, a Bryant surface is a 2-dimensional surface embedded in 3-dimensional hyperbolic space with constant mean curvature equal to 1.[1][2] These surfaces take their name from the geometer Robert Bryant, who proved that every simply-connected minimal surface in 3-dimensional Euclidean space is isometric to a Bryant surface by a holomorphic parameterization analogous to the (Euclidean) Weierstrass–Enneper parameterization.[3] References1. ^{{citation | last1 = Collin | first1 = Pascal | last2 = Hauswirth | first2 = Laurent | last3 = Rosenberg | first3 = Harold | arxiv = math/0105265 | doi = 10.2307/2661364 | issue = 3 | journal = Annals of Mathematics | mr = 1836284 | pages = 623–659 | series = Second Series | title = The geometry of finite topology Bryant surfaces | volume = 153 | year = 2001}}. {{differential-geometry-stub}}2. ^{{citation | last = Rosenberg | first = Harold | contribution = Bryant surfaces | doi = 10.1007/978-3-540-45609-4_3 | location = Berlin | mr = 1901614 | pages = 67–111 | publisher = Springer | series = Lecture Notes in Math. | title = The global theory of minimal surfaces in flat spaces (Martina Franca, 1999) | volume = 1775 | year = 2002}}. 3. ^{{citation | last = Bryant | first = Robert L. | issue = 154-155 | journal = Astérisque | mr = 955072 | pages = 12, 321–347, 353 (1988) | title = Surfaces of mean curvature one in hyperbolic space | year = 1987}}. 3 : Hyperbolic geometry|Riemannian geometry|Minimal surfaces |
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