53 citations · 228 across the 24 of their papers we have counts for
27 papers
Jordan curves inscribe a positive measure of rectangles
Joshua Evan Greene, Andrew Lobb
Suppose that is a Jordan curve of diameter which encloses a region of area . We prove that there exists a subset of measure at least…
On the values taken by slice torus invariants
Peter Feller, Lukas Lewark, Andrew Lobb
We study the space of slice-torus invariants. In particular we characterize the set of values that slice-torus invariants may take on a given knot in terms of the stable smooth sli…
Squeezed Knots
Peter Feller, Lukas Lewark, Andrew Lobb
Squeezed knots are those knots that appear as slices of genus-minimizing oriented smooth cobordisms between positive and negative torus knots. We show that this class of knots is l…
Cyclic quadrilaterals and smooth Jordan curves
Joshua Evan Greene, Andrew Lobb
For every smooth Jordan curve and cyclic quadrilateral in the Euclidean plane, we show that there exists an orientation-preserving similarity taking the vertices of to…
The Rectangular Peg Problem
Joshua Evan Greene, Andrew Lobb
For every smooth Jordan curve and rectangle in the Euclidean plane, we show that there exists a rectangle similar to whose vertices lie on . The proof relies on Shev…
Threaded rings that swim in excitable media
Antonio Cincotti, Fabian Maucher, David Evans +6
Cardiac tissue and the Belousov-Zhabotinsky reaction provide two notable examples of excitable media that support scroll waves, in which a filament core is the source of spiral wav…