We are concerned with the global weak rigidity of the Gauss–Codazzi–Ricci (GCR)
equations on Riemannian manifolds and the corresponding isometric immersions of …

We establish the weak continuity of the Gauss-Coddazi-Ricci system for isometric
embedding with respect to the uniform $ L^ p $-bounded solution sequence for $ p> 2 …

The isometric immersion of two-dimensional Riemannian manifolds or surfaces with
negative Gauss curvature into the three-dimensional Euclidean space is studied in this …

REGULARITY OF SUBELLIPTIC MONGE-AMP`ERE EQUATIONS IN THE PLANE 1. Introduction
There is a vast body of elliptic regularity resul Page 1 TRANSACTIONS OF THE AMERICAN …

In this paper, we study the smooth isometric immersion of a complete simply connected
surface with a negative Gauss curvature in the three-dimensional Euclidean space. For a …

The Gromov-Hausdorff hyperspace of nonnegatively curved 2-spheres Page 1 PROCEEDINGS
OF THE AMERICAN MATHEMATICAL SOCIETY Volume 146, Number 4, April 2018, Pages …

The classical Efimov theorem states that there is no C 2-smoothly immersed complete
surface in R 3 with negative Gauss curvature uniformly separated from zero. Here we …

The isometric immersion of two-dimensional Riemannian manifolds with negative Gauss
curvature into the three-dimensional Euclidean space is considered through the Gauss …

We prove that a smooth compact submanifold of codimension 2 immersed in R n, n≥ 3,
bounds at most finitely many topologically distinct, compact, nonnegatively curved …

The isometric immersion of two-dimensional Riemannian manifolds or surfaces in the three-
dimensional Euclidean space is a fundamental problem in differential geometry. When the …