35 citations · 111 across the 11 of their papers we have counts for
13 papers
Typechecking without Minimum Types: Finite Bases and Backward Checking for
Mingkun Xiao, Yixuan Sun
System has decidable subtyping but lacks minimum types. We prove that typechecking is decidable for arbitrary explicitly annotated terms with unrestricted subsumpti…
The conjugate locus in convex 3-manifolds
Thomas Waters, Matthew Cherrie
In this paper we study the conjugate locus in convex manifolds. Our main tool is Jacobi fields, which we use to define a special coordinate system on the unit sphere of the tangent…
The normal map as a vector field
Thomas Waters, Matthew Cherrie
In this paper we consider the normal map of a closed plane curve as a vector field on the cylinder. We interpret the critical points geometrically and study their Poincaré index, i…
The conjugate locus on convex surfaces
Thomas Waters
The conjugate locus of a point on a surface is the envelope of geodesics emanating radially from that point. In this paper we show that the conjugate loci of generic points on conv…
Integrable geodesic flows on tubular sub-manifolds
Thomas Waters
In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dim…
Bifurcations of the conjugate locus
Thomas Waters
The conjugate locus of a point in a surface will have a certain number of cusps. As the point is moved in the surface the conjugate locus may spontaneously ga…