Zhenxiao Xie

activity

20122026

most citedMoebius geometry of three dimensional Wintgen ideal submanifolds in S^5

16 citations · 21 across the 11 of their papers we have counts for

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12 papers · 1 filter

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

On the first eigenvalue of the area Jacobi operator for complex curves in Kähler surfaces

Zhenxiao Xie

In this paper, we investigate the first eigenvalue $Λ_{1}$ of the area Jacobi operator for complex curves in Kähler surfaces, establishing an extrinsic counterpart to the classical L…

math.DG2026

Two classes of Willmore Surfaces in $S^{2} \times S^{2}$

Xiaoling Chai, Shimpei Kobayashi, Changping Wang +1

We establish two classification theorems for Willmore surfaces in $S^{2} \times S^{2}$ . Firstly, we prove that a Willmore surface which is also minimal must be either…

math.DG2023

Willmore surfaces in 4-dimensional conformal manifolds

Changping Wang, Zhenxiao Xie

This paper is dedicated to the exploration of the conformal Willmore functional for surfaces within 4-dimensional conformal manifolds. We provide a detailed calculation of both the…

math.DG2023

Classification of Minimal Immersions of Conformally Flat $3$ -Tori and $4$ -Tori in Spheres by The First Eigenfunctions

Ying Lv, Peng Wang, Zhenxiao Xie

This paper is devoted to the study of minimal immersions of flat $n$ -tori into spheres, especially those immersed by the first eigenfunctions (such immersion is called $λ_{1}$ -minima…

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

On the first eigenvalue of the area Jacobi operator for complex curves in Kähler surfaces

Two classes of Willmore Surfaces in S2×S2

Willmore surfaces in 4-dimensional conformal manifolds

Classification of Minimal Immersions of Conformally Flat 3-Tori and 4-Tori in Spheres by The First Eigenfunctions

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 $C P^{2}$

Two classes of Willmore Surfaces in $S^{2} \times S^{2}$

Classification of Minimal Immersions of Conformally Flat $3$ -Tori and $4$ -Tori in Spheres by The First Eigenfunctions