Hongda Qiu

collaborators

4 papers

math.DG2026

On the curvature bounded sphere problem in $R^{3}$

Hongda Qiu

We prove that if a topological sphere smoothly embedded into $R^{3}$ with normal curvatures absolutely bounded by $1$ is contained in an open ball of radius $2$ , then the re…

math.DG2025

On equivariant isometric embeddings of Riemannian manifolds with symmetries

Hongda Qiu

Let $(M, g)$ be a $C^{\infty}$ -smooth, $n$ -dimensional Riemannian manifold which is diffeomorphic to $\RR^n$ and admit an action of a properly discontinuous and cocompact group. This…

math.DG2025

Supersqueezed sphere

Hongda Qiu

This work pose an example of a smooth closed surface in $R^{3}$ which has genus $0$ , normal curvatures at most $1$ in absolute value and encloses a volume smaller than the v…

math.DG2025

On the geometry of Riemannian isometric embeddings

Dmitri Burago, Hongda Qiu

This note pertains to isometric embeddings endowed with certain geometric properties. We study two embedding problems for a Riemannian manifold $M$ which is diffeomorphic to $\RR^n…

On the curvature bounded sphere problem in R3

On equivariant isometric embeddings of Riemannian manifolds with symmetries

Supersqueezed sphere

On the geometry of Riemannian isometric embeddings

On the curvature bounded sphere problem in $R^{3}$