Bryant surface

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]

References
  1. Collin, Pascal; Hauswirth, Laurent; Rosenberg, Harold (2001), "The geometry of finite topology Bryant surfaces", Annals of Mathematics, Second Series, 153 (3): 623–659, arXiv:math/0105265, Bibcode:2001math......5265C, doi:10.2307/2661364, JSTOR 2661364, MR 1836284, S2CID 15020316.
  2. Rosenberg, Harold (2002), "Bryant surfaces", The global theory of minimal surfaces in flat spaces (Martina Franca, 1999), Lecture Notes in Math., vol. 1775, Berlin: Springer, pp. 67–111, doi:10.1007/978-3-540-45609-4_3, MR 1901614.
  3. Bryant, Robert L. (1987), "Surfaces of mean curvature one in hyperbolic space", Astérisque (154–155): 12, 321–347, 353 (1988), MR 0955072.


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