arXiv subjects

Zexuan Ouyang

Publications and source records attributed to Zexuan Ouyang.

4 recordsLinked to original sources

arXiv2026

A positively curved metric on the Gromoll-Meyer sphere

We construct an explicit deformation of the bi-invariant metric on Sp(2) whose induced metrics on the Gromoll-Meyer exotic 7-sphere have positive sectional curvature for all sufficiently small positive parameters. The deformation is determined by a fixed self-adjoint operator compatible with the quotient action. The proof combines a uniform curvature estimate with an algebraic analysis of the horizontal commuting planes. On the critical set where the lower-order positive terms vanish, we establish an explicit positive lower bound for the cubic coefficient of the curvature numerator. Uniform control of the fourth-order remainder and a compactness argument then show that every sectional curvature is positive

math.DG↗

arXiv2026

Metric Degenerations and Satake Compactification of Enriques Surfaces

We determine the Gromov--Hausdorff compactification of the moduli space of unit-diameter Ricci-flat Kähler metrics on Enriques surfaces. We show that all metric degenerations are encoded by the adjoint Satake compactification of the Enriques period domain. There are 32 boundary components added in this Satake compactification, and the GH limit at each boundary is determined. As a corollary, all the GH limits of Kähler Ricci-flat metrics on Enriques surfaces are classified, including those for a fixed complex structure or a fixed polarization.

math.DG↗

arXiv2026

Compactification of metric moduli space of $K3$ surfaces

We prove a conjecture of Odaka--Oshima, which says that there is an algebraic description of the Gromov--Hausdorff compactification of all unit-diameter hyperkähler metrics on K3 surfaces. As a corollary, we obtain a classification of the Gromov--Hausdorff limits of those hyperkähler K3 surfaces with a fixed complex structure or with a fixed polarization.

math.DG↗

arXiv2025

Collapsing of K3 Surfaces and Special Kähler Structures

We study the structure of $\mathfrak{M}_2$, the set of half-dimensional collapsing spaces of hyperkähler metrics on K3 surfaces. We show that $\mathfrak{M}_2$ consists precisely of those underlying metric spaces of integral singular special Kähler structures (SKSs) on $ \mathbb{P}^1 $. Furthermore, we establish a bijection between integral singular SKSs on $\mathbb{P}^1 $ and Jacobian elliptic K3 surfaces with a marked holomorphic volume form. Additionally, we compute the number of Jacobian elliptic K3 surfaces that correspond to a given metric on $ \mathbb{P}^1 $.

math.DG↗