TY - JOUR
T1 - Lojasiewicz inequality for weighted homogeneous polynomial with isolated singularity
AU - Tan, Shengli
AU - Yau, Stephen S.T.
AU - Zuo, Huaiqing
PY - 2010/11
Y1 - 2010/11
N2 - Let δf be a gradient vector field of a weighted homogenous polynomial with isolated critical point at the origin. Let (w1, . . . ,wn) be the weights of f. In this paper, we prove that the Łojasiewicz Exponent θ of f is precisely equal to max 0≤i≤n wi - 1. This means that for some constant c, |δf(z)| ≥ c|z|θ in a neighborhood of 0, which provides the optimal lower estimate of |δf(z)|.
AB - Let δf be a gradient vector field of a weighted homogenous polynomial with isolated critical point at the origin. Let (w1, . . . ,wn) be the weights of f. In this paper, we prove that the Łojasiewicz Exponent θ of f is precisely equal to max 0≤i≤n wi - 1. This means that for some constant c, |δf(z)| ≥ c|z|θ in a neighborhood of 0, which provides the optimal lower estimate of |δf(z)|.
UR - https://www.scopus.com/pages/publications/78149240819
U2 - 10.1090/S0002-9939-2010-10387-8
DO - 10.1090/S0002-9939-2010-10387-8
M3 - 文章
AN - SCOPUS:78149240819
SN - 0002-9939
VL - 138
SP - 3975
EP - 3984
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 11
ER -