46 citations · 151 across the 23 of their papers we have counts for
31 papers
Axis-parallel square packing with an exact formula for optimal packing of seven squares
Matthew Badger
How large a square is needed to hold axis-parallel squares of prescribed side lengths? We give exact formulas for the optimal side through seven squares, with explicit construction…
Method I revisited: extension, continuity, and applications
Matthew Badger
Carathéodory's construction, also known as Method I, turns any weight on a family of sets into an outer measure. The difficulty is the extension problem: showing that the outer mea…
Space-filling surfaces: sharp Hölder continuous parameterizations from squares to cubes
Matthew Badger, Kevin Palmer
Following a hint of Semmes, we employ Stong's bijections between integer lattices to construct space-filling surfaces, which are higher-dimensional analogues of space-filling curve…
Tangents to Lipschitz and Sobolev images
Matthew Badger, Jared Krandel, Vyron Vellis
We develop geometric versions of Rademacher and Calderon type differentiability theorems in two categories. A special case of our results is that for any Lipschitz or continuous $W…
On the number of nodal domains of homogeneous caloric polynomials
Matthew Badger, Cole Jeznach
We investigate the minimum and maximum number of nodal domains across all time-dependent homogeneous caloric polynomials of degree in (space $\…
Square packings and rectifiable doubling measures
Matthew Badger, Raanan Schul
We prove that for all integers , there exists doubling measures on with full support that are -rectifiable and purely -unrectifiable in th…