The symplectic Hadamard question

2026/07/14 by Dan Cristofaro-Gardiner · 1 voice
Mathematics · #math.SG

paper · pdf

Abstract

We show that a simply connected symplectic manifold admitting a complete nonpositively curved compatible metric is symplectomorphic to R²ⁿ with its standard symplectic form. This answers the "symplectic Hadamard question" of McDuff-Salamon in the affirmative.

Citations

• Quantitative Darboux theorems in contact geometry
• Potential Theory on Almost Complex Manifolds
• Lectures on Holomorphic Curves in Symplectic and Contact Geometry
• Tightness in contact metric 3-manifolds

Discussions

• Dan Cristofaro-Gardiner: The symplectic Hadamard question https://arxiv.org/abs/2607.12940 https://arxiv.org/pdf/2607.12940 https://arxiv.org/html/2607.12940 [bsky, 0 points, 0 comments]

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