On the number of singular points for planar multivalued harmonic functions
Francesco Ghiraldin, Luca Spolaor
TL;DR
This paper provides a quantitative estimate on the number of singular points of multiplicity Q for 2D Q-valued energy minimizing maps, based on the analysis of their frequency function.
Contribution
It introduces a new estimate linking the count of singular points to the frequency function for multivalued harmonic functions in two dimensions.
Findings
Quantitative bounds on singular points based on frequency function
Application to multivalued harmonic functions in 2D
Enhanced understanding of singularity distribution
Abstract
In this note we give a quantitative estimate on the number of singular points of multiplicity of a -dimensional -valued energy minimizing map, in terms of the value of its frequency function.
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Taxonomy
TopicsAnalytic and geometric function theory · Nonlinear Partial Differential Equations · Mathematical Approximation and Integration