Peng Wang

activity

20242026

collaborators

13 papers

math.DG2026

On the Willmore energy of flat $n$ -tori in $R^{N}$ and Chen's conjecture for $n$ -tori

Ruijie Ni, Peng Wang, Zhenxiao Xie

This paper establishes the sharp lower bound $(4 n π^{2})^{n /2}$ for the Willmore energy $W$ of flat $n$ -tori in the Euclidean space. Up to Möbius transformations, the Cliffo…

math.DG2026

A proof of the Willmore-type conjecture in $C P^{2}$

Peng Wang, Zhenxiao Xie, Chen Zhao

In 2002, Montiel and Urbano conjectured that the Clifford torus in $C P^{2}$ minimizes the Willmore-type functional $W^{-} = \int_{T^{2}} (2 + ∣ H ∣^{2}) d A,$ either among all…

math.DG2026

The isoperimetric inequality and CMC hypersurfaces in Cartan-Hadamard manifolds

Shibing Chen, Mohammad Ghomi, Peng Wang

We show that the sharp Euclidean isoperimetric inequality holds for domains in complete simply connected Riemannian $n$ -manifolds of nonpositive sectional curvature, $3 \leq n \leq 9$ …

math.DG2026

The Cartan-Hadamard conjecture in dimension five

Shibing Chen, Mohammad Ghomi, Peng Wang

We show that the sharp Euclidean isoperimetric inequality holds for domains in complete simply connected Riemannian $5$ -manifolds of nonpositive sectional curvature, which establis…

math.DG2025

Classification of Willmore $2$ -spheres in $S^{n}$

Xiang Ma, Franz Pedit, Peng Wang

This paper resolves a long-standing open problem by providing a classification of Willmore $2$ -spheres in $S^{n}$ . We show that any such $2$ -sphere is either totally isotropic--origi…

math.NA2025

Convergence Analysis of a Stochastic Interacting Particle-Field Algorithm for 3D Parabolic-Parabolic Keller-Segel Systems

Boyi Hu, Zhongjian Wang, Jack Xin +1

Chemotaxis models describe the movement of organisms in response to chemical gradients. In this paper, we present a stochastic interacting particle-field algorithm with a random ba…

math.DG2024

Gauss maps of Möbius surfaces in the $n$ -dimensional sphere

David Brander, Shimpei Kobayashi, Peng Wang

In this note we discuss Gauss maps for Möbius surfaces in the $n$ -sphere, and their applications in the study of Willmore surfaces. One such ``Gauss map'', naturally associated to…

math.DG2024

The Willmore problem for surfaces with symmetry

Rob Kusner, Ying Lü, Peng Wang

The Willmore Problem seeks closed surfaces in $S^{3} \subset R^{4}$ of a given topological type minimizing the squared-mean-curvature energy $W = \int |H_{\mathbb{R}^4}…

math.DG2024

Harmonic maps of finite uniton number into inner symmetric spaces via based normalized extended frames

Josef F. Dorfmeister, Peng Wang

In this paper, we develop a loop group description of harmonic maps $F : M \to G / K$ of finite uniton number, from a Riemann surface $M,$ compact or non-compact, in…

math.DG2024

Algebraic Harmonic Maps, Totally Symmetric Harmonic Maps and a Conjecture

Josef F. Dorfmeister, Peng Wang

In this paper, we discuss the associated family of harmonic maps $F : M \to G / K$ from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact t…

math.DG2024

Equivariant primitive harmonic maps into $k -$ symmetric spaces, with applications to Willmore surfaces

Josef F. Dorfmeister, Peng Wang

In this note we discuss the construction of equivariant primitive harmonic maps into $k -$ symmetric spaces and give many applications to the construction of Willmore surfaces. In pa…

math.DG2024

On the index of minimal hypersurfaces in $S^{n + 1}$ with $λ_{1} < n$

Hang Chen, Peng Wang

In this paper, we prove that a closed minimal hypersurface in $\SSS$ with $λ_{1} < n$ has Morse index at least $n + 4$ , providing a partial answer to a conjecture of Perdomo. As a coroll…

math.DG2024

Willmore surfaces in spheres via loop groups: a survey

Josef F. Dorfmeister, Peng Wang

In the past decades, the authors made some systematic research on global and local properties of Willmore surfaces in terms of the DPW method. In this note we give a survey, mainly…

On the Willmore energy of flat n-tori in RN and Chen's conjecture for n-tori

A proof of the Willmore-type conjecture in CP2

The isoperimetric inequality and CMC hypersurfaces in Cartan-Hadamard manifolds

The Cartan-Hadamard conjecture in dimension five

Classification of Willmore 2-spheres in Sn

Convergence Analysis of a Stochastic Interacting Particle-Field Algorithm for 3D Parabolic-Parabolic Keller-Segel Systems

Gauss maps of Möbius surfaces in the n-dimensional sphere

The Willmore problem for surfaces with symmetry

Harmonic maps of finite uniton number into inner symmetric spaces via based normalized extended frames

Algebraic Harmonic Maps, Totally Symmetric Harmonic Maps and a Conjecture

Equivariant primitive harmonic maps into k−symmetric spaces, with applications to Willmore surfaces

On the index of minimal hypersurfaces in Sn+1 with λ1​<n

Willmore surfaces in spheres via loop groups: a survey

On the Willmore energy of flat $n$ -tori in $R^{N}$ and Chen's conjecture for $n$ -tori

A proof of the Willmore-type conjecture in $C P^{2}$

Classification of Willmore $2$ -spheres in $S^{n}$

Gauss maps of Möbius surfaces in the $n$ -dimensional sphere

Equivariant primitive harmonic maps into $k -$ symmetric spaces, with applications to Willmore surfaces

On the index of minimal hypersurfaces in $S^{n + 1}$ with $λ_{1} < n$