Tittle: Partial regularity for Lipschitz solutions to the minimal surface system Abstract: The minimal surface system is the Euler-Lagrange system for the area functional of a high codimension graph and reduces to the minimal surface equation in the case that the codimension is one. Though the regularity theory for the minimal surface equation is well understood, […]
Title: The Lawson-Osserman conjecture for the minimal surface systemAbstract: In their seminal work on the minimal surface system, Lawson and Osserman conjectured that Lipschitz graphs that are critical points of the area functional with respect to outer variations are also critical with respect to domain variations. We will discuss the proof of this conjecture for […]
Title: The Nevo-Thangavelu spherical maximal function on two step nilpotent Lie groups.Consider R^d times R^m with the group structure of a 2-step Carnot Lie group and natural parabolic dilations. The maximal operator originally introduced by Nevo and Thangavelu in the setting of the Heisenberg groups is generated by (noncommutative) convolution associated with measures on […]
Title: Optimal observability times for wave and Schrodinger equations on really simple domainsAbstract: Observability for evolution equations asks: if I take a partial measurement in a system, can it “see” some physical quantity, such as energy? In a series of papers with E. Stafford, Z. Lu, and S. Carpenter, we showed that energy for the […]