Yusheng Wang

activity

20102024

most citedFinite Quotient of Join in Alexandrov Geometry

2 citations · 4 across the 15 of their papers we have counts for

collaborators

15 papers

math.DG2024

A Schur's type volume comparison theorem

Xiaole Su, Yi Tan, Yusheng Wang

In this paper, inspired by Schur's comparison theorem about curves in Euclidean space, we mainly provide a Schur's type volume comparison theorem, which is about the volumes of the…

math.DG2024

An Index III lemma and Rauch III theorem & applications

Shengqi Hu, Xiaole Su, Yusheng Wang

Inspired by Index I and II lemmas and Rauch I and II theorems, we formulate out an Index III lemma and Rauch III theorem in this paper. As applications, we present a Rauch's type t…

math.DG2022

A proof of Toponogov's theorem in Alexandrov geometry

Shengqi Hu, Xiaole Su, Yusheng Wang

This paper aims to give an elementary proof for Toponogov's theorem in Alexandrov geometry with lower curvature bound. The idea of the proof comes from the fact that, in Riemannian…

math.DG2021

New definitions of Alexandrov space and applications

Shengqi Hu, Xiaole Su, Yusheng Wang

In this paper we show that, in the definition of Alexandrov spaces with lower or upper curvature bound, the original conditions can be replaced with much weaker ones. For the purpo…

math.MG2020

Quasi-convex subsets and the farthest direction in Alexandrov spaces with lower curvature bound

Xiaole Su, Hongwei Sun, Yusheng Wang

This paper aims to give a further study on quasi-convex subsets in Alexandrov spaces with lower curvature bound which are introduced in [SSW]. We first provide new insights on quas…

math.MG2020

Quasi-convex subsets in Alexandrov spaces with lower curvature bound

Xiaole Su, Hongwei Sun, Yusheng Wang

In this paper, we introduce quasi-convex subsets in Alxandrov spaces with lower curvature bound, which include not only all closed convex subsets without boundary but also all extr…

math.MG2019

Pythagorean Theorem & curvature with lower or upper bound

Xiaole Su, Hongwei Sun, Yusheng Wang

In this paper, we give a comparison version of Pythagorean Theorem to judge the lower or upper bound of the curvature of Alexandrov spaces (including Riemannian manifolds).

math.DG2018

A Schur-Toponogov theorem in Riemannian geometry & a new proof of Toponogov's theorem in Alexandrov geometry

Yusheng Wang

In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by it…

math.MG2018

The Soul Conjecture in Alexandrov Geometry in dimension 4

Xiaochun Rong, Yusheng Wang

In this paper, we prove the Soul Conjecture in Alexandrov geometry in dimension $4$ , i.e. if $X$ is a complete non-compact $4$ -dimensional Alexandrov space of non-negative curvatur…

math.MG2016★ 2 cited

Finite Quotient of Join in Alexandrov Geometry

Xiaochun Rong, Yusheng Wang

Given two $n_{i}$ -dimensional Alexandrov spaces $X_{i}$ of curvature $\geq 1$ , the join of $X_{1}$ and $X_{2}$ is an $(n_{1} + n_{2} + 1)$ -dimensional Alexandrov space $X$ of curvature $\geq 1$ , whi…

math.DG2015

An Isometrical $CP^{n}$ -Theorem

Xiaole Su, Hongwei Sun, Yusheng Wang

Let $M^{n} (n \geq 3)$ be a complete Riemannian manifold with $sec_{M} \geq 1$ , and let $M_{i}^{n_{i}}$ ( $i = 1, 2$ ) be two comlplete totally geodesic submanifolds in $M$ . We prove that if $n_…

math.DG2015

On the Blaschke's Conjecture

Xiaole Su, Hongwei Sun, Yusheng Wang

The Blaschke's conjecture asserts that if $\diam(M)=\text{Inj}(M)=\frac\pi2$ (up to a rescaling) for a complete Riemannian manifold $M$ , then $M$ is isometric to $\Bbb S^n(\frac12)…

math.DG2014

On $\frac{π}{2}$ -separated subsets of Alexandrov spaces with curvature $\geq 1$

Xiaole Su, Hongwei Sun, Yusheng Wang

Let $M$ be an $n$ -dimensional Alexandrov space with curvature $\geq 1$ , and let ${q_{1}, \dots, q_{k}}$ be any $\frac{π}{2}$ -separated subset in $M$ (i.e. the distance $|q_iq_j|\geq\fra…

math.MG2013

Rigidity theorems for glued spaces being suspensions, cones and joins in Alexandrov geometry with curvature bounded below

Xiaole Su, Hongwei Sun, Yusheng Wang

In the paper, we give rigidity theorems when the glued space of two Alexandrov spapces with curvature bounded below is a suspension, cone or join. And we list some basic properties…

math.DG2010★ 2 cited

On Almost Isometry Theorem in Alexandrov Spaces with Curvature Bounded Below

Xiaole Su, Hongwei Sun, Yusheng Wang

In this paper we give a new proof for an almost isometry theorem in Alexandrov spaces with curvature bounded below.

A Schur's type volume comparison theorem

An Index III lemma and Rauch III theorem & applications

A proof of Toponogov's theorem in Alexandrov geometry

New definitions of Alexandrov space and applications

Quasi-convex subsets and the farthest direction in Alexandrov spaces with lower curvature bound

Quasi-convex subsets in Alexandrov spaces with lower curvature bound

Pythagorean Theorem & curvature with lower or upper bound

A Schur-Toponogov theorem in Riemannian geometry & a new proof of Toponogov's theorem in Alexandrov geometry

The Soul Conjecture in Alexandrov Geometry in dimension 4

Finite Quotient of Join in Alexandrov Geometry

An Isometrical CPn-Theorem

On the Blaschke's Conjecture

On 2π​-separated subsets of Alexandrov spaces with curvature ≥1

Rigidity theorems for glued spaces being suspensions, cones and joins in Alexandrov geometry with curvature bounded below

On Almost Isometry Theorem in Alexandrov Spaces with Curvature Bounded Below

An Isometrical $CP^{n}$ -Theorem

On $\frac{π}{2}$ -separated subsets of Alexandrov spaces with curvature $\geq 1$