Entire solutions of Donaldson's equation
Weiyong He
TL;DR
This paper constructs numerous nontrivial entire solutions to Donaldson's equation and proves a Liouville type theorem, advancing understanding of the solution space and suggesting potential classification of all solutions.
Contribution
It introduces a method to generate many solutions and establishes a Liouville theorem, providing new insights into the structure of solutions to Donaldson's equation.
Findings
Constructed infinite many nontrivial entire solutions
Proved a Liouville type theorem for entire solutions
Suggested the possibility of classifying all solutions
Abstract
In this short note we shall construct infinite many nontrivial entire solutions to Donaldson's equation. We shall also prove a Liouville type theorem for entire solutions of the Donaldson equation. We believe that one should be able to classify all entire solutions of the Donaldson equation.
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Taxonomy
TopicsGeometry and complex manifolds · Meromorphic and Entire Functions · Algebraic Geometry and Number Theory