Solvability of a class of fully nonlinear elliptic equations on tori
Elia Fusi
TL;DR
This paper investigates the conditions under which certain fully nonlinear elliptic equations can be solved on flat tori, with applications to Calabi-Yau problems in torus bundles.
Contribution
It establishes solvability results for a class of nonlinear elliptic equations on tori, connecting geometric analysis with complex geometry.
Findings
Proved existence of solutions under specific conditions.
Linked nonlinear PDE solvability to geometric structures.
Extended previous results to new classes of equations.
Abstract
We study the solvability of a class of fully nonlinear equations on the flat torus. The equations arise in the study of some Calabi-Yau type problems in torus bundles.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Black Holes and Theoretical Physics