Contraction of areas vs. topology of mappings

Abstract

We construct homotopically non-trivial maps from the unit m-sphere to the unit (m-1)-sphere with arbitrarily small k-dilation for each k greater than (m + 1)/2. We prove that homotopically non-trivial maps from the unit m-sphere to the unit (m-1)-sphere cannot have arbitrarily small k-dilation for k less than or equal to (m + 1)/2.

82 pages. Typos corrected. Reference added to a recent paper of Wenger and Young. Accepted for publication in Geometric and Functional Analysis

References in corpus (2)

• Lipschitz minimality of Hopf fibrations and Hopf vector fields
• Isoperimetric inequalities and rational homotopy invariants

Cited by in corpus (1)

• Lipschitz homotopy groups of the Heisenberg groups