Generalized Kazdan-Warner equations on foliated manifolds
Natsuo Miyatake
TL;DR
This paper extends the Kazdan-Warner theorem to compact foliated manifolds, solving generalized PDEs including the transverse Hitchin equation for harmonic metrics on Higgs bundles, with new existence and uniqueness results.
Contribution
It generalizes the Kazdan-Warner theorem to foliated manifolds and solves new classes of PDEs like the transverse Hitchin equation in this context.
Findings
Existence and uniqueness of solutions on foliated manifolds
Solutions to transverse Hitchin equations for Higgs bundles
Examples of PDEs solved in the foliated setting
Abstract
On compact foliated manifolds, we extend the theorem on the existence and uniqueness of solutions to generalized Kazdan-Warner equations. We provide examples of PDEs that we solve, including the transverse Hitchin equation for a diagonal harmonic metric on basic cyclic Higgs bundles over a 3-dimensional complex codimension one foliated manifold, and its generalizations.
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Taxonomy
TopicsGeometry and complex manifolds · Nonlinear Waves and Solitons · Black Holes and Theoretical Physics