SINGLY-PERIODIC MINIMAL SURFACES IN H2 × R
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We construct three kinds of complete embedded singly-periodic minimal surfaces in $\mathbb{H}^2{\times}\mathbb{R}$. The first one is a 1-parameter family of minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the second one is a 2-parameter family of minimal surfaces which has a fundamental piece of finite total curvature and is asymptotic to a finite number of vertical planes; the last one is a 2-parameter family of minimal surfaces which fill $\mathbb{H}^2{\times}\mathbb{R}$ by finite Scherk's towers.
Abstract
We construct three kinds of complete embedded singly-periodic minimal surfaces in $\mathbb{H}^2{\times}\mathbb{R}$. The first one is a 1-parameter family of minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the second one is a 2-parameter family of minimal surfaces which has a fundamental piece of finite total curvature and is asymptotic to a finite number of vertical planes; the last one is a 2-parameter family of minimal surfaces which fill $\mathbb{H}^2{\times}\mathbb{R}$ by finite Scherk's towers.
참고문헌 (14)
- J. Choe, "Embedded minimal surfaces and total curvature of curves in a manifold", Math. Res. Lett, 10(2), pp.343~362 (2003)
- B. Daniel, "Isometric immersions into Sn × R and Hn × R and applications to minimal surfaces", Trans. Amer. Math. Soc, 361(12), pp.6255~6282 (2009)
- L. Hauswirth, "Minimal surfaces of Riemann type in three-dimensional product mani- folds", Pacific J. Math, 224(1), pp.91~117 (2006)
- L. Hauswirth, "Associate and conjugate minimal immer- sions in M ×R", Tohoku Math. J. (2), 60(2), pp.267~286 (2008)
- "Tiling the hyperbolic plane"[URL]
- H. Karcher, "Embedded minimal surfaces derived from Scherk's examples", Manuscripta Math, 62(1), pp.83~114 (1988)
- Y. Kim, "Helicoids in S2 × R and H2 × R", Pacific J. Math, 242(2), pp.281~297 (2009)
- F. Morabito, "Saddle tower in H2 × R", Journal de l'Institut de Mathematiques de Jussieu
- C. B. Morrey, "The problem of Plateau on a Riemannian manifold", Ann. of Math. (2), 49, pp.807~851 (1948)
- B. Nelli, "Minimal surfaces in H2 × R", Bull. Braz. Math. Soc. (N.S.), 33(2), pp.263~292 (2002)
- J. Pyo, "New complete embedded minimal surfaces in H2 × R", Ann. Global Anal. Geom, 40(2), pp.167~176 (2011)
- H. Rosenberg, "Minimal surfaces in M2 × R", Illinois J. Math, 46(4), pp.1177~1195 (2002)
- R. Sa Earp, "Screw motion surfaces in H2 × R and S2 × R", Illinois J. Math, 49(4), pp.1323~1362 (2005)
- R. Schoen, "Uniqueness, symmetry, and embeddedness of minimal surfaces", J. Differen- tial Geom, 18(4), pp.791~809 (1983)