75 citations · 334 across the 43 of their papers we have counts for
4 papers · 1 filter
The deformed Hermitian-Yang-Mills equation in geometry and physics
Tristan C. Collins, Dan Xie, Shing-Tung Yau
We provide an introduction to the mathematics and physics of the deformed Hermitian-Yang-Mills equation, a fully nonlinear geometric PDE on Kahler manifolds which plays an importan…
The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics
Tristan C. Collins, Tomoyuki Hisamoto, Ryosuke Takahashi
We introduce the inverse Monge-Ampere flow as the gradient flow of the Ding energy functional on the space of Kahler metrics in for . We prove the long-time e…
Log-canonical thresholds in real and complex dimension 2
Tristan C. Collins
We study the set of log-canonical thresholds (or critical integrability indices) of holomorphic (resp. real analytic) function germs in (resp. ). In pa…
Dimension of the minimum set for the real and complex Monge-Ampère equations in critical Sobolev spaces
Tristan C. Collins, Connor Mooney
We prove that the zero set of a nonnegative plurisubharmonic function that solves in and is in $W^{2, \frac{n(n-k)}{k}…