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arxiv math/0607083 v1 pith:Y4DMYNSQ submitted 2006-07-04 math.DG math.SG

Two-forms on four-manifolds and elliptic equations

S. K. Donaldson This is my paper
classification math.DG math.SG
keywords ellipticequationssomeclasscomplexconnectionsdefinediscuss
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We define a general class of elliptic equations for 2-forms on 4-manifolds, of which the complex Monge-Ampere equation is a prototype. We obtain some regularity results and discuss various connections (some speculative) with modern symplectic 4-manifold theory.

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Cited by 2 Pith papers

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  1. Four-dimensional Riemannian geometry via 2-forms

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    A description of 4D Riemannian geometry via 2-forms valued in an SO(3) bundle from SU(2)-structures, yielding a unique invariant functional with Einstein critical points.

  2. Special Lagrangian submanifolds and circle collapse on K3

    math.DG 2026-06 unverdicted novelty 5.0

    Constructs degenerating special Lagrangian two-spheres and tori in collapsing K3 surfaces that lift from affine lines on a three-dimensional base, including connections between Taub-NUT bubbles.