Noncompact L_p-Minkowski problems
نویسندگان
چکیده
In this paper we prove the existence of complete, noncompact convex hypersurfaces whose $p$-curvature function is prescribed on a domain in unit sphere. This problem related to solvability Monge-Ampere type equations subject certain boundary conditions depending value $p$. The special case $p=1$ was previously studied by Pogorelov and Chou-Wang. Here, give some sufficient for general $p\neq1$.
منابع مشابه
Minkowski Problems for Complete Noncompact Convex Hypersurfaces
LetX be a compact, strictly convex C-hypersurface in the (n+1)-dimensional Euclidean space R. The Gauss map ofX maps the hypersurface one-to-one and onto the unit n-sphere S. One may parametrize X by the inverse of the Gauss map. Consequently, the Gauss curvature can be regarded as a function on S. The classical Minkowski problem asks conversely when a positive function K on S is the Gauss curv...
متن کاملStrong Vector Equilibrium Problems on Noncompact Sets
In this paper, by using the famous Brouwer fixed point theorem, some existence theorems of strong efficient solutions for the strong vector equilibrium problems are obtained on noncompact sets of general real Hausdorff topological vector spaces without assuming that the dual of the ordering cone has a weak∗ compact base. Moreover, the closeness and the convexity of the strong efficient solution...
متن کاملGluing and Moduli for Noncompact Geometric Problems
The existence results we discuss for each of these problems are ones whereby known solutions (sometimes satisfying certain nondegeneracy hypotheses) are glued together to produce new solutions. Although this sort of procedure is quite well-known, there have been some recent advances on which we wish to report here. We also discuss what has been established about the moduli spaces of all solutio...
متن کاملInterior Estimates and Longtime Solutions for Mean Curvature Flow of Noncompact Spacelike Hypersurfaces in Minkowski Space
Spacelike hypersurfaces with prescribed mean curvature have played a major role in the study of Lorentzian manifolds Maximal mean curvature zero hypersurfaces were used in the rst proof of the positive mass theorem Constant mean curvature hypersurfaces provide convenient time gauges for the Einstein equations For a survey of results we refer to In and it was shown that entire solutions of the m...
متن کاملInverse additive problems for Minkowski sumsets I
We give the structure of discrete two-dimensional finite sets A, B ⊆ R2 which are extremal for the recently obtained inequality |A + B| ≥ ( |A| m + |B| n − 1)(m + n − 1), where m and n are the minimum number of parallel lines covering A and B respectively. Via compression techniques, the above bound also holds when m is the maximal number of points of A contained in one of the parallel lines co...
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: Indiana University Mathematics Journal
سال: 2021
ISSN: ['1943-5258', '0022-2518', '1943-5266']
DOI: https://doi.org/10.1512/iumj.2021.70.8432