Zi-Yu Li

A Hadamard Formula for Equilibrium Envelopes under Parallel Deformation

Let $(X,\omega_0)$ be a compact K\"ahler manifold of complex dimension $n$, and let $U\Subset X$ have $C^{3,1}$ uniformly strongly pseudoconvex boundary. Consider the signed parallel family $U_t=\{\rho<t\}$, where $\rho$ is a defining function agreeing near $\partial U$ with the signed distance, negative in $U$. Let $u...