Let X be the limit of an inverse system {Xα, παβ, ∧} and and let λ be the cardinal number of A. Assume that each projection πα ： X → Xα is an open and onto map and X is A-paracompact. We prove that if each ...Let X be the limit of an inverse system {Xα, παβ, ∧} and and let λ be the cardinal number of A. Assume that each projection πα ： X → Xα is an open and onto map and X is A-paracompact. We prove that if each Xα is B（LF, ω^2）-refinable （hereditarily B（LF, ω^2）- refinable）, then X is B（LF, ω^2）-refinable （hereditarily B（LF,ω ^2）-refinable）. Furthermore, we show that B（LF, ω^2）-refinable spaces can be preserved inversely undcr closed maps.展开更多
This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are...This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are with assumptions on lower bound of the m-Bakry-Emery Ricci curvature for p=1.These are weighted version for the corresponding results of the present author(J.Math.Anal.Appl.,2020,490).展开更多
基金Supported by the National Natural Science Foundation of China (10671173)
文摘Let X be the limit of an inverse system {Xα, παβ, ∧} and and let λ be the cardinal number of A. Assume that each projection πα ： X → Xα is an open and onto map and X is A-paracompact. We prove that if each Xα is B（LF, ω^2）-refinable （hereditarily B（LF, ω^2）- refinable）, then X is B（LF, ω^2）-refinable （hereditarily B（LF,ω ^2）-refinable）. Furthermore, we show that B（LF, ω^2）-refinable spaces can be preserved inversely undcr closed maps.
基金Partially supported by National Science Foundation of China(11426195,11771377)Natural Science Foundation of Jiangsu Province(BK20191435)。
文摘This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are with assumptions on lower bound of the m-Bakry-Emery Ricci curvature for p=1.These are weighted version for the corresponding results of the present author(J.Math.Anal.Appl.,2020,490).
