17 citations · 77 across the 17 of their papers we have counts for
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Interpolating between Hausdorff and box dimension
Amlan Banaji
Hausdorff and box dimension are two familiar notions of fractal dimension. Box dimension can be larger than Hausdorff dimension, because in the definition of box dimension, all set…
Dimensions of popcorn-like pyramid sets
Amlan Banaji, Haipeng Chen
This article concerns the dimension theory of the graphs of a family of functions which include the well-known 'popcorn function' and its pyramid-like higher-dimensional analogues.…
Metric Spaces where Geodesics are Never Unique
Amlan Banaji
This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimising geodesics. We pro…
Attainable forms of intermediate dimensions
Amlan Banaji, Alex Rutar
The intermediate dimensions are a family of dimensions which interpolate between the Hausdorff and box dimensions of sets. We prove a necessary and sufficient condition for a given…
Generalised intermediate dimensions
Amlan Banaji
We introduce a family of dimensions, which we call the -intermediate dimensions, that lie between the Hausdorff and box dimensions and generalise the intermediate dimensions int…