The equation of prescribed Gauss curvature without boundary conditions
نویسندگان
چکیده
منابع مشابه
On the Existence and Regularity of Hypersurfaces of Prescribed Gauss Curvature with Boundary
In this paper we study the Dirichlet problem for some Monge-Ampère type equations on S, which naturally arise in some geometric problems. The result then is applied to prove the existence of hypersurfaces in R of prescribed Gauss-Kronecker curvature and with fixed boundary.
متن کاملThe Equation of Prescribed Ricci Curvature
Introduction. In [5], J. Milnor cited "understanding the Ricci tensor Rik = J^ Rt'kl 9J as a fundamental problem of present-day mathematics. A basic issue, then, is to determine which symmetric covariant tensors of rank two can be Ricci tensors of Riemannian metrics. The definition of Ricci curvature casts the problem of finding a metric g which realizes a given Ricci curvature R as one of solv...
متن کاملSubharmonic solutions of the prescribed curvature equation∗
We study the existence of subharmonic solutions of the prescribed curvature equation − ( u′/ √ 1 + u′ )′ = f(t, u). According to the behaviour at zero, or at infinity, of the prescribed curvature f , we prove the existence of arbitrarily small classical subharmonic solutions, or bounded variation subharmonic solutions with arbitrarily large oscillations. 2010 Mathematics Subject Classification:...
متن کاملHypersurfaces of Prescribed Gauss Curvature in Exterior Domains
We prove an existence theorem for convex hypersurfaces of prescribed Gauß curvature in the complement of a compact set in Euclidean space which are close to a cone.
متن کاملEntire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space
which gives an isometric embedding of the hyperbolic space H into R. Hano and Nomizu [11] were probably the first to observe the non-uniqueness of isometric embeddings of H in R by constructing other (geometrically distinct) entire solutions of (1.1)–(1.2) for n 1⁄4 2 (and c1 1) using methods of ordinary di¤erential equations. Using the theory of Monge-Ampère equations, A.-M. Li [12] studied en...
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: Journal of Differential Geometry
سال: 1984
ISSN: 0022-040X
DOI: 10.4310/jdg/1214439282