13 citations · 17 across the 6 of their papers we have counts for
7 papers
A Poincaré ball model for taxicab hyperbolic geometry
Aaron Fish, Dylan Helliwell
Taxicab space is a modification of Euclidean space that uses an alternative notion of distance. Similarly, the Poincaré ball is a model of hyperbolic geometry that consists of a su…
Further Study on Domains and Quasihyperbolic Distances
Shusen Ding, Dylan Helliwell, Gavin Pandya +1
We establish constructive geometric tools for determining when a domain is -averaging and obtain upper and lower bounds for the -integrals of the quasihyperbolic distance…
Apollonian sets in taxicab geometry
Eric Bahuaud, Shana Crawford, Aaron Fish +6
Fix two points and in the plane and a positive number . A result credited to Apollonius of Perga states that the set of points that satisfy $d(x, p)/d(x, q) =…
Bach Flow on Homogeneous Products
Dylan Helliwell
Qualitative behavior of Bach flow is established on compact four-dimensional locally homogeneous product manifolds. This is achieved by lifting to the homogeneous universal cover a…
Uniqueness for Some Higher-Order Geometric Flows
Eric Bahuaud, Dylan Helliwell
We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With t…
Short-time existence for some higher-order geometric flows
Eric Bahuaud, Dylan Helliwell
We establish short-time existence and regularity for higher-order flows generated by a class of polynomial natural tensors that, after an adjustment by the Lie derivative of the me…