Luke G. Rogers

activity

20062026

most citedDerivations and Dirichlet forms on fractals

45 citations · 146 across the 29 of their papers we have counts for

collaborators

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9 papers · 1 filter

math.CA2020

Resistance Scaling on $4 N$ -Carpets

Claire Canner, Christopher Hayes, Shinyu Huang +2

The $4 N$ carpets are a class of infinitely ramified self-similar fractals with a large group of symmetries. For a $4 N$ -carpet $F$ , let ${F_{n}}_{n \geq 0}$ be the natural decreasin…

math.CA2019★ 1 cited

Geodesic Interpolation on Sierpinski Gaskets

Caitlin M. Davis, Laura A. LeGare, Cory W. McCartan +1

We study the analogue of a convex interpolant of two sets on Sierpinski gaskets and an associated notion of measure transport. The structure of a natural family of interpolating me…

math.CA2019

Harmonic Gradients on Higher Dimensional Sierpinski Gaskets

Luke Brown, Giovanni Ferrer, Gamal Mograby +2

We consider criteria for the differentiability of functions with continuous Laplacian on the Sierpinski Gasket and its higher-dimensional variants $S G_{N}$ , $N > 3$ , proving results th…

math.CA2017★ 5 cited

Spectra of Magnetic Operators on the Diamond Lattice Fractal

Antoni Brzoska, Aubrey Coffey, Madeline Rooney +2

We adapt the well-known spectral decimation technique for computing spectra of Laplacians on certain symmetric self-similar sets to the case of magnetic Schrodinger operators and w…

math.CA2017★ 1 cited

Measurable Riemannian structure on higher dimensional harmonic Sierpinski gaskets

Sara Chari, Joshua Frisch, Daniel J. Kelleher +1

We prove existence of a measurable Riemannian structure on higher-dimensional harmonic Sierpinski gasket fractals and deduce Gaussian heat kernel bounds in the geodesic metric. Our…

math.CA2010

Estimates for the resolvent kernel of the Laplacian on p.c.f. self similar fractals and blowups