http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
STABLE MINIMAL HYPERSURFACES IN THE HYPERBOLIC SPACE
서검교 대한수학회 2011 대한수학회지 Vol.48 No.2
In this paper we give an upper bound of the rst eigenvalue of the Laplace operator on a complete stable minimal hypersurface M in the hyperbolic space which has nite L^2-norm of the second fundamental form on M. We provide some sufficient conditions for minimal hypersurface of the hyperbolic space to be stable. We also describe stability of catenoids and helicoids in the hyperbolic space. In particular, it is shown that there exists a family of stable higher-dimensional catenoids in the hyperbolic space.
Sphere-foliated minimal and constant mean curvature hypersurfaces in product spaces
서검교 대한수학회 2011 대한수학회보 Vol.48 No.2
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.
REGULARITY OF SOAP FILM-LIKE SURFACES SPANNING GRAPHS IN A RIEMANNIAN MANIFOLD
Robert Gulliver,박성호,표준철,서검교 대한수학회 2010 대한수학회지 Vol.47 No.5
Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant −κ2. Using the cone total curvature TC(Γ) of a graph ¡ which was introduced by Gulliver and Yamada [8], we prove that the density at any point of a soap film-like surface Σ spanning a graph ¡ Γ M is less than or equal to [수식]. From this density estimate we obtain the regularity theorems for soap film-like surfaces spanning graphs with small total curvature. In particular, when n = 3,this density estimate implies that if [수식] then the only possible singularities of a piecewise smooth (M, 0, δ)-minimizing set Σ are the Y -singularity cone. In a manifold with sectional curvature bounded above by b2 and diameter bounded by π/b, we obtain similar results for any soap film-like surfaces spanning a graph with the corresponding bound on cone total curvature.