Publisher: College of Information Science and Technology  

Date: December 10, 2024

Huang Hongzhi, a faculty member at the College of Information Science and Technology at Jinan University, has made a significant contribution to the field of mathematics with the independent publication of his research paper titled Finite generation of fundamental groups for manifolds with non-negative Ricci curvature whose universal cover is almost polar at infinity in the esteemed journal Journal für die reine und angewandte Mathematik (Crelle's Journal). 

(Screenshot of the paper)

Crelle's Journal, a leading SCI journal recognized as a T1 mathematics journal by the Chinese Mathematical Society, holds the distinction of being the oldest continuously published mathematical journal in the world. It has a storied history of publishing influential works, including Abel's groundbreaking proof regarding the non-existence of root solutions for general fifth-order equations, which addressed a longstanding problem in mathematics.

Huang's paper delves into Riemannian geometry, focusing on the interplay between curvature and the shape of space. Ricci curvature, a key geometric quantity, has gained prominence in recent research. Notably, significant advancements have been made in this area, including Brue Naber Semola's recent refutation of the Milnor conjecture, a problem that had remained unresolved for nearly six decades.

In his article, Huang proves that the fundamental group π1(M) of a complete open manifold M with non-negative Ricci curvature is finitely generated, contingent upon the Riemannian universal cover ?M satisfying an “almost k-polar at infinity” condition. He further establishes that this fundamental group is virtually abelian and demonstrates that the base point of any tangent cone at infinity of such a manifold is nearly a pole. Additionally, if ?M exhibits almost maximal Euclidean volume growth, Huang shows that M deformation retracts to a closed submanifold F that is diffeomorphic to a flat manifold, provided M is not simply connected.

For more details, the article can be accessed [here]

(https://www.degruyter.com/document/doi/10.1515/crelle-2024-0089/html).