Intersection homology theory via rectifiable currents

Qinglan Xia
April 2004
Calculus of Variations & Partial Differential Equations;Apr2004, Vol. 19 Issue 4, p421
Academic Journal
Here is given a rectifiable currents? version of intersection homology theory on stratified subanalytic pseudomanifolds. This new version enables one to study some variational problems on stratified subanalytic pseudomanifolds. We first achieve an isomorphism between this rectifiable currents? version and the version using subanalytic chains. Then we define a suitably modified mass on the complex of rectifiable currents to ensure that each sequence of subanalytic chains with bounded modified mass has a convegent subsequence and the limit rectifiable current still satisfies the perversity condition of the approximating chains. The associated mass minimizers turn out to be almost minimal currents and this fact leads to some regularity results.


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