33 citations · 41 across the 6 of their papers we have counts for
7 papers
First variation of the fractional -dimensional measure: extending the concept of nonlocal curvature to submanifolds
Cornelia Mihaila, Brian Seguin
The fractional -dimensional measure of a submanifold of is a generalization of the fractional perimeter and fractional length appearing in the literature and depe…
A definition of fractional k-dimensional measure: bridging the gap between fractional length and fractional area
Cornelia Mihaila, Brian Seguin
Here we introduce a fractional notion of -dimensional measure, , that depends on a parameter that lies between and . When this coincides with the f…
Bubbling with -almost constant mean curvature and an Alexandrov-type theorem for crystals
M. G. Delgadino, F. Maggi, C. Mihaila +1
A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measu…
On the shape of capillarity droplets in a container
Francesco Maggi, Cornelia Mihaila
We provide a quantitative description of global minimizers of the Gauss free energy for a liquid droplet bounded in a container in the small volume regime.
Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences
Ilya Amburg, Krishna Dasaratha, Laure Flapan +6
The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit…
Cubic Irrationals and Periodicity via a Family of Multi-dimensional Continued Fraction Algorithms
Krishna Dasaratha, Laure Flapan, Thomas Garrity +5
We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic…
A Generalized Family of Multidimensional Continued Fractions: TRIP Maps
Krishna Dasaratha, Laure Flapan, Thomas Garrity +5
Most well-known multidimensional continued fractions, including the Mönkemeyer map and the triangle map, are generated by repeatedly subdividing triangles. This paper constructs a…