7 citations · 23 across the 6 of their papers we have counts for
6 papers · 1 filter
Isoperimetric inequalities and rational homotopy invariants
Larry Guth
We estimate the linear isoperimetric constants of an n-dimensional ellipse. Using these estimates and a technique of Gromov, we estimate the Hopf and linking invariants of Lipschit…
Directional isoperimetric inequalities and rational homotopy invariants
Larry Guth
We estimate the second order linking invariants of Lipschitz maps from an n-dimensional ellipse. The estimate uses a new directionally-dependent version of the isoperimetric inequa…
Area-expanding embeddings of rectangles
Larry Guth
We estimate whether there is an embedding from one n-dimensional rectangle into another which expands every k-dimensional area. Our estimate is sharp up to a constant factor in eac…
Homotopically non-trivial maps with small k-dilation
Larry Guth
We construct homotopically non-trivial maps from S^m to S^n with arbitrarily small 3-dilation for certain pairs (m,n). The simplest example is m=4, n=3. Other examples include arbi…
Minimax problems related to cup powers and Steenrod squares
Larry Guth
If F is a family of mod 2 flat k-cycles in the unit n-ball, we lower bound the maximal volume of any cycle in F in terms of the homology class of F in the space of all cycles. We g…
Lipshitz maps from surfaces
Larry Guth
We give a simple procedure to estimate the smallest Lipshitz constant of a degree 1 map from a Riemannian 2-sphere to the unit 2-sphere, up to a factor of 10. Using this procedure,…