On a problem of Yau regarding a higher dimensional generalization of the Cohn-Vossen inequality

TL;DR

This paper demonstrates that Yau's proposed problem regarding a higher-dimensional generalization of the Cohn-Vossen inequality is false in general, providing counterexamples based on recent work by Wu and Zheng.

Contribution

It shows that Yau's problem does not hold universally and constructs counterexamples using recent advances by Wu and Zheng.

Findings

Yau's problem is false in higher dimensions

Counterexamples are constructed based on Wu and Zheng's work

The result clarifies limitations of the higher-dimensional Cohn-Vossen inequality

Abstract

We show that a problem by Yau can not be true in general. The counterexamples are constructed based on the recent work of Wu and Zheng.