TY - JOUR
T1 - Dimension estimate of polynomial growth harmonic forms
AU - Ray Chen, Jui Tang
AU - Anna Sung, Chiung Jue
PY - 2006
Y1 - 2006
N2 - Let Hpl (M) be the space of polynomial growth harmonic forms. We proved that the dimension of such spaces must be finite and can be estimated if the metric is uniformly equivalent to one with a nonnegative curvature operator. In particular, this implies that the space of harmonic forms of fixed growth order on the Euclidean space with any periodic metric must be finite dimensional.
AB - Let Hpl (M) be the space of polynomial growth harmonic forms. We proved that the dimension of such spaces must be finite and can be estimated if the metric is uniformly equivalent to one with a nonnegative curvature operator. In particular, this implies that the space of harmonic forms of fixed growth order on the Euclidean space with any periodic metric must be finite dimensional.
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U2 - 10.4310/jdg/1146680515
DO - 10.4310/jdg/1146680515
M3 - Article
AN - SCOPUS:33745441067
SN - 0022-040X
VL - 73
SP - 167
EP - 183
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
IS - 1
ER -