Rigidity of the sharp Bezout estimate on nonnegatively curved Riemann surfaces

TL;DR

This paper demonstrates the rigidity of a sharp Bezout estimate on nonnegatively curved Riemann surfaces using a three circle theorem, confirming the estimate's uniqueness under these conditions.

Contribution

It establishes the rigidity of Liu's sharp Bezout estimate specifically for nonnegatively curved Riemann surfaces, utilizing a novel application of the three circle theorem.

Findings

Rigidity of the sharp Bezout estimate proven

Application of the three circle theorem to Riemann surfaces

Confirmation of Liu's estimate uniqueness

Abstract

In this short note, by using a general three circle theorem, we show the rigidity of the sharp Bezout estimate first found by Gang Liu on nonnegatively curved Riemann surface.