Methods and Applications of Analysis

Volume 24 (2017)

Number 1

Special issue dedicated to Henry B. Laufer on the occasion of his 70th birthday: Part 1

Guest Editors: Stephen S.-T. Yau (Tsinghua University, China); Gert-Martin Greuel (University of Kaiserslautern, Germany); Jonathan Wahl (University of North Carolina, USA); Rong Du (East China Normal University, China); Yun Gao (Shanghai Jiao Tong University, China); and Huaiqing Zuo (Tsinghua University, China)

Nine characterizations of weighted homogeneous isolated hypersurface singularities

Pages: 155 – 167



Stephen S.-T. Yau (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Huai Qing Zuo (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)


This survey paper discusses many different ways of characterizations of weighted homogeneous (quasi-homogeneity) isolated hypersurface singularities.


weighted homogeneous, isolated singularity, invariants

2010 Mathematics Subject Classification

14B05, 14J17

Research partially supported by NSFC (grant nos. 11531007, 11771231, 11401335), start-up fund from Tsinghua University and Tsinghua University Initiative Scientific Research Program.

Received 3 February 2016

Published 18 August 2017