Affiliation:
1. Department of Mathematics, Rutgers University, Frelinghuysen Road, Piscataway, NJ, USA
Abstract
Abstract
We consider a priori estimates of Weyl’s embedding problem of $(\mathbb{S}^2, g)$ in general three-dimensional Riemannian manifold $(N^3, \bar g)$. We establish interior $C^2$ estimate under natural geometric assumption. Together with a recent work by Li and Wang [18], we obtain an isometric embedding of $(\mathbb{S}^2,g)$ in Riemannian manifold. In addition, we reprove Weyl’s embedding theorem in space form under the condition that $g\in C^2$ with $D^2g$ Dini continuous.
Funder
China Scholarship Council
Publisher
Oxford University Press (OUP)
Reference35 articles.
1. Elliptic equations in divergence form, geometric critical points of solutions, and Stekloff eigenfunctions;Alessandrini;SIAM J. Math. Anal.,1994
2. On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications;Bers,1955
3. Quasilocal energy and conserved charges derived from the gravitational action;Brown;Phys Rev. D (3),1993
4. The Weyl problem with nonnegative Gauss curvature in hyperbolic space;Chang;Canad. J. Math.,2015
5. Regularity of an isometric imbedding of a two-dimensional Riemannian manifold into a three-dimensional Riemannian space, (Russian) Ukrain;Dubrovin;Geometr. Sb. Vyp.,1966
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Weyl estimates for spacelike hypersurfaces in de Sitter space;Pacific Journal of Mathematics;2022-10-16
2. A free boundary isometric embedding problem in the unit ball;Calculus of Variations and Partial Differential Equations;2022-02-03
3. A Pu–Bonnesen inequality;Journal of Geometry;2021-04-15
4. The Weyl problem of isometric immersions revisited;Bulletin of the London Mathematical Society;2020-09-07
5. Capacity, quasi-local mass, and singular fill-ins;Journal für die reine und angewandte Mathematik (Crelles Journal);2019-12-19