5 papers
Optimal regularity of optimal transport and degenerations of convex cones
Tristan C. Collins, Benjy Firester, Freid Tong
If is an optimal transport map between bounded convex domains and , we characterize the regularity/singularity dichotomy for at $(x,T(x)) \in \partial Ω\times \par…
Shrinking Kähler-Ricci solitons on toric fano fibrations
Tristan C. Collins, Genggeng Huang, Freid Tong +1
We prove that a smooth toric Fano fibration admits a complete gradient shrinking Kähler-Ricci soliton.
Homogeneous optimal transport maps between oblique cones
Tristan C. Collins, Benjy Firester, Freid Tong
We construct homogeneous optimal transport maps for the quadratic cost between convex cones with homogeneous, possibly degenerate, densities when the cones satisfy an obliqueness c…
On a general class of free boundary Monge-Ampère equations
Tristan C. Collins, Benjy Firester
We solve a general class of free boundary Monge-Ampère equations given by \[ \det D^2u = λ\dfrac{f(-u)}{g(u^\star)h(\nabla u)}χ_{\{u<0\}} \; \text{ in } \mathbb{R}^n, \quad \nabla…
Boundary regularity of optimal transport maps on convex domains
Tristan C. Collins, Freid Tong
We study the regularity of optimal transport maps between convex domains with quadratic cost. For nondegenerate Dini continuous densities, we prove -regularity of the pote…