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Sphere-foliated minimal and constant mean curvature hypersurfaces in product spaces

서검교
대한수학회 (The Korean Mathematical Society)|2011.03|대한수학회보 (Bulletin of the KMS)|제48권 제2호|pp. 335-342

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키워드

product spacefoliationconstant mean curvaturerotationally symmetric hypersurface
주제분류수학

초록

In this paper, we prove that minimal hypersurfaces when n≥3 and nonzero constant mean curvature hypersurfaces when n≥2 foliated by spheres in parallel horizontal hyperplanes in H^n R must be rotationally symmetric.

Abstract

In this paper, we prove that minimal hypersurfaces when n≥3 and nonzero constant mean curvature hypersurfaces when n≥2 foliated by spheres in parallel horizontal hyperplanes in H^n R must be rotationally symmetric.

참고문헌 (13)

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  8. R. Lopez, "Constant mean curvature hypersurfaces foliated by spheres", Differential Geom. Appl, 11(3), pp.245~256 (1999)
  9. B. Nelli, "Minimal surfaces in H2×R", Bull. Braz. Math. Soc. (N.S.), 33(2), pp.263~292 (2002)
  10. B. Nelli, "Uniqueness of H-surfaces in H2×R, jHj 1=2, with boundary one or two parallel horizontal circles", Ann. Global Anal. Geom, 33(4), pp.307~321 (2008)
  11. 박성호, "Sphere-foliated minimal and constant mean curvature hypersurfaces in space forms and Lorentz-Minkowski space", ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 32(3), pp.1019~1044 (2002), ROCKY MT MATH CONSORTIUM
  12. R. Sa Earp, "Screw motion surfaces in H2×R and S2×R", Illinois J. Math, 49(4), pp.1323~1362 (2005)
  13. S. Stahl, "The Poincare Half-Plane" (1993), Jones and Bartlett Publishers

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