Tong Wang

activity

20222026

collaborators

11 papers

math.DG2026

Embedded minimal $S^{1}$ -bundles in $S^{4}$

Tongrui Wang

We construct infinitely many embedded minimal hypersurfaces of pairwise distinct irreducible topological types in the unit $4$ -sphere $S^{4}$ , which provides a new answer to…

math.DG2026

Infinite existence of equivariant minimal hypersurfaces

Xingzhe Li, Tongrui Wang

For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show that there are infinitely many $G$ -invariant minimal hypersurfaces. Under the assump…

math.DG2026

Equivariant min-max theory and the spherical Bernstein problem in $S^{4}$

Tongrui Wang, Zhichao Wang, Xin Zhou

We construct an embedded non-equatorial minimal hypersphere in the unit $4$ -sphere $S^{4}$ , which provides a new resolution of Chern's spherical Bernstein problem in $\mathb…

math.DG2026

Multiplicity one for equivariant min-max theory in prescribed homology classes

Tongrui Wang

For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show a generic multiplicity one theorem in equivariant min-max theory, and show in generi…

math.DG2024

Minimal surfaces with low genus in lens spaces

Xingzhe Li, Tongrui Wang, Xuan Yao

Given a Riemannian $RP^{3}$ with a bumpy metric or a metric of positive Ricci curvature, we show that there either exist four distinct minimal real projective planes, or exi…

math.DG2023

Generalized $S^{1}$ -stability theorem

Tongrui Wang, Xuan Yao

We use the equivariant $μ$ -bubbles technique to prove that for any compact manifold $M^{n}$ with non-empty boundary, $n \in {3, 5, 6}$ , the Yamabe invariant of $M^{n}$ is positive if and…

math.DG2023

Improved Hebey-Vaugon conjecture on equivariant Yamabe invariants in dimension 3

Tongrui Wang, Xuan Yao

Consider a closed connected $3$ -manifold $M$ acted diffeomorphically on by a compact Lie group $G$ with at least one orbit of finite cardinality. We show an upper bound for the $G$ …

math.DG2023

Generic density of equivariant min-max hypersurfaces

Tongrui Wang

For a compact Riemannian manifold $M^{n + 1}$ acted isometrically on by a compact Lie group $G$ with cohomogeneity $Cohom (G) \geq 2$ , we show the Weyl asymptotic law for the $G$ …

math.DG2023

Equivariant min-max hypersurface in $G$ -manifolds with positive Ricci curvature

Tongrui Wang

In this paper, we consider a connected orientable closed Riemannian manifold $M^{n + 1}$ with positive Ricci curvature. Suppose $G$ is a compact Lie group acting by isometries on $M$ …

math.DG2022

Equivariant Morse index of min-max $G$ -invariant minimal hypersurfaces

Tongrui Wang

For a closed Riemannian manifold $M^{n + 1}$ with a compact Lie group $G$ acting as isometries, the equivariant min-max theory gives the existence and the potential abundance of mini…

math.DG2022

Min-max theory for free boundary G-invariant minimal hypersurfaces

Tongrui Wang

Given a compact Riemannian manifold $M^{n + 1}$ with dimension $3 \leq n + 1 \leq 7$ and $\partial M \neq = \emptyset$ , the free boundary min-max theory built by Martin Man-Chun Li and Xin Z…

Embedded minimal S1-bundles in S4

Infinite existence of equivariant minimal hypersurfaces

Equivariant min-max theory and the spherical Bernstein problem in S4

Multiplicity one for equivariant min-max theory in prescribed homology classes

Minimal surfaces with low genus in lens spaces

Generalized S1-stability theorem

Improved Hebey-Vaugon conjecture on equivariant Yamabe invariants in dimension 3

Generic density of equivariant min-max hypersurfaces

Equivariant min-max hypersurface in G-manifolds with positive Ricci curvature

Equivariant Morse index of min-max G-invariant minimal hypersurfaces

Min-max theory for free boundary G-invariant minimal hypersurfaces

Embedded minimal $S^{1}$ -bundles in $S^{4}$

Equivariant min-max theory and the spherical Bernstein problem in $S^{4}$

Generalized $S^{1}$ -stability theorem

Equivariant min-max hypersurface in $G$ -manifolds with positive Ricci curvature

Equivariant Morse index of min-max $G$ -invariant minimal hypersurfaces