Isoperimetric Inequalities of Euclidean Type in Metric Spaces
نویسنده
چکیده
1.1. Statement of the main result. The isoperimetric problem of euclidean type for a space X and given classes Ik−1, Ik, and Ik+1 of surfaces of dimension k − 1, k, and k + 1 in X , together with boundary operators Ik+1 ∂ −→ Ik ∂ −→ Ik−1 and a volume function M on each class, asks the following: Does there exist for every surface T ∈ Ik without boundary, ∂T = 0, a surface S ∈ Ik+1 with ∂S = T and such that M(S) ≤ DM(T ) k+1
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