11 citations · 29 across the 15 of their papers we have counts for
13 papers · 1 filter
A simple proof of Perelman's collapsing theorem for 3-manifolds
Jianguo Cao, Jian Ge
We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point the…
Perelman's collapsing theorem for 3-manifolds
Jianguo Cao, Jian Ge
We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex ana…
Minimal volume and simplicial norm of visibility n-manifolds and compact 3-manifolds
Jianguo Cao, Xiaoyang Chen
Theorem A. Let denote a closed Riemannian manifold with nonpositive sectional curvature and let be the universal cover of with the lifted metric. Suppose t…
The modified Calabi-Yau problems for CR-manifolds and applications
JIanguo Cao, Shu-Cheng Chang
In this paper, we derive a partial result related to a question of Yau: "Does a simply-connected complete Kähler manifold M with negative sectional curvature admit a bounded non-co…
An optimal extension of Perelman's comparison theorem for quadrangles and its applications
Jianguo Cao, Bo Dai, Jiaqiang Mei
In this paper we discuss an extension of Perelman's comparison for quadrangles. Among applications of this new comparison theorem, we study the equidistance evolution of hypersurfa…
An extension of Perelman's soul theorem for singular spaces
Jianguo Cao, Bo Dai, Jiaqiang Mei
In this paper, we study open complete metric spaces with non-negative curvature. Among other things, we establish an extension of Perelman's soul theorem for possibly singular spac…
Certain 4-manifolds with non-negative sectional curvature
Jianguo Cao
In this paper, we study certain compact 4-manifolds with non-negative sectional curvature . If is the scalar curvature and is the self-dual part of Weyl tensor, then i…
Pseudo-Einstein and Q-flat metrics with eigenvalue estimates on CR-hypersurfaces
Jianguo Cao, Shu-Cheng Chang
Let be the smooth boundary of a bounded strongly pseudo-convex domain in a complete Stein manifold . Then (1) For , admits a pseudo-Eiste…
The d-bar-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in CP^n with n>= 3
Jianguo Cao, Mei-Chi Shaw
A Lipschitz hypersurface is a hypersurface which locally is the graph of a Lipschitz function. A Lipschitz (or C^1) hypersurface is said to be Levi-flat if it is locally foliated b…
An intrinsic proof of Gromoll-Grove diameter rigidity theorem
Jianguo Cao, Hongyan Tang
We will present a new proof of the Gromoll-Grove diameter rigidity theorem.
Martin points on open manifolds of non-positive curvature
Jianguo Cao, Huijun Fan, Francois Ledrappier
The Martin boundary of a Cartan-Hadamard manifold describes a fine geometric structure at infinity, which is a sub-space of positive harmonic functions. We describe conditions whic…
The smoothness of Riemannian submersions with nonnegative sectional curvature
Jianguo Cao, Mei-Chi Shaw
Let be a complete, non-compact and -smooth Riemannian manifold with nonnegative sectional curvature. Suppose $\Cal S$ is a soul of . Then any distance non-incr…
Estimates for the -Neumann problem and nonexistence of Levi-flat hypersurfaces in
Jianguo Cao, Mei-Chi Shaw, Lihe Wang
Let be a pseudoconvex domain with -smooth boundary in . We prove that the N(p,q)Ω$. Furthermore, th…