Contraction of Areas vs. Topology of Mappings
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We construct homotopically non-trivial maps from S[superscript m] to S[superscript m−1] with arbitrarily small k-dilation for each k > [(m + 1) over 2]. We prove that homotopically non-trivial maps from S[superscript m] to S[superscript m−1] cannot have arbitrarily small k-dilation for k ≤ [(m + 1) over 2].
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Geometric and Functional Analysis
Guth, Larry. “Contraction of Areas Vs. Topology of Mappings.” Geometric and Functional Analysis 23, no. 6 (December 2013): 1804–1902.