On the Gauss map of minimal surfaces with finite total curvature
نویسندگان
چکیده
منابع مشابه
On the Gauss Curvature of Minimal Surfaces!?)
1. Summary of results. The following is known: let 5 be a minimal surface defined by z=f(x, y) over the region D:x2+y2<R2, and let p be the point of S over the origin. Let W= (1+fl+fl)112 at p. Then the Gauss curvature K at p satisfies \K\ Sc/R2W2. The best numerical value of c known previously was 12.25. This inequality is simultaneously sharpened and generalized. First of all, it is proved th...
متن کاملComplete Embedded Minimal Surfaces of Finite Total Curvature
2 Basic theory and the global Weierstrass representation 4 2.1 Finite total curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 The example of Chen-Gackstatter . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Embeddedness and finite total curvature: necessary conditions . . . . . . . 20 2.3.1 Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملOn Complete Nonorientable Minimal Surfaces with Low Total Curvature
We classify complete nonorientable minimal surfaces in R3 with total curvature −8π.
متن کاملAn Estimate for the Gauss Curvature of Minimal Surfaces in R Whose Gauss Map Omits a Set of Hyperplanes
We give an estimate of the Gauss curvature for minimal surfaces in Rm whose Gauss map omits more than m(m + 1)/2 hyperplanes in P(C).
متن کاملL_1 operator and Gauss map of quadric surfaces
The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1991
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700029658