Add to ORKGGromov and Sormani conjectured that a sequence of three dimensional Riemannian manifolds with nonnegative scalar curvature and some additional uniform geometric bounds should have a subsequence which converges in some sense to a limit space with generalized notion of nonnegative scalar curvature. In this paper, we study the pre-compactness of a sequence of three dimensional warped product manifolds with warped circles over standard $\mathbb{S}^2$ that have nonnegative scalar curvature, a uniform upper bound on the volume, and a positive uniform lower bound on the MinA, which is the minimum area of closed minimal surfaces in the manifold. We prove that such a sequence has a subsequence converging to a $W^{1, p}$ Riemannian metric for all $p<...
By using Gromov's $\mu$-bubble technique, we show that the $3$-dimensional spherical caps are rigid ...
We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing...
In this work we establish a sharp geometric inequality for closed hypersurfaces in complete noncompa...
Gromov and Sormani conjectured that a sequence of three dimensional Riemannian manifolds with nonneg...
Gromov and Sormani conjectured that sequences of compact Riemannian manifolds with nonnegative scala...
We show that a complete non-compact 3-manifold with scalar curvature bounded below by a positive con...
In this paper we prove the scalar curvature extremality and rigidity for a class of warped product s...
Here we survey the compactness and geometric stability conjectures formulated by the participants at...
In this thesis, we develop a new method of performing surgery on 3-dimensional manifolds called sew...
For sequences of warped product metrics on a 3-torus satisfying the scalar curvature bound Rj = -1j,...
We study the prescribed scalar curvature problem in a conformal class on orbifolds with isolated sin...
In this paper, we give some $C^{0}$ or $C^{1}$ limit theorems for total scalar curvatures. More prec...
Examples show that Riemannian manifolds with almost-Euclidean lower bounds on scalar curvature and P...
On closed hyperbolic manifolds of dimension $n\geq 3$, we review the definition of the average area ...
Following Gromov, a Riemannian manifold is called area-extremal if any modification that increases s...
By using Gromov's $\mu$-bubble technique, we show that the $3$-dimensional spherical caps are rigid ...
We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing...
In this work we establish a sharp geometric inequality for closed hypersurfaces in complete noncompa...
Gromov and Sormani conjectured that a sequence of three dimensional Riemannian manifolds with nonneg...
Gromov and Sormani conjectured that sequences of compact Riemannian manifolds with nonnegative scala...
We show that a complete non-compact 3-manifold with scalar curvature bounded below by a positive con...
In this paper we prove the scalar curvature extremality and rigidity for a class of warped product s...
Here we survey the compactness and geometric stability conjectures formulated by the participants at...
In this thesis, we develop a new method of performing surgery on 3-dimensional manifolds called sew...
For sequences of warped product metrics on a 3-torus satisfying the scalar curvature bound Rj = -1j,...
We study the prescribed scalar curvature problem in a conformal class on orbifolds with isolated sin...
In this paper, we give some $C^{0}$ or $C^{1}$ limit theorems for total scalar curvatures. More prec...
Examples show that Riemannian manifolds with almost-Euclidean lower bounds on scalar curvature and P...
On closed hyperbolic manifolds of dimension $n\geq 3$, we review the definition of the average area ...
Following Gromov, a Riemannian manifold is called area-extremal if any modification that increases s...
By using Gromov's $\mu$-bubble technique, we show that the $3$-dimensional spherical caps are rigid ...
We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing...
In this work we establish a sharp geometric inequality for closed hypersurfaces in complete noncompa...