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

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9 papers · 1 filter

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.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.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.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

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

An Isometrical CPn-Theorem

On the Blaschke's Conjecture

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

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 $\geq 1$