Bryant surface

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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, ISBN   978-3-540-43120-6, 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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