6 papers
Regularity theorems for Lipschitz viscosity solutions to the minimal surface system
Bryan Dimler
We prove several regularity theorems concerning Lipschitz viscosity solutions to the minimal surface system. The main lemma (i.e. ``Decoupling Lemma") says that the component funct…
Special Lagrangians with multiple isolated singularities
Bryan Dimler, Filippo Gaia
We extend the Caffarelli-Hardt-Simon perturbation argument for truncated regular minimal cones to the special Lagrangian setting and prove a bridge principle for regular special La…
Uniqueness in the Plateau problem for calibrated currents
Bryan Dimler, Chen-Kuan Lee
We show that every compactly supported smoothly calibrated integral current with connected boundary is the unique solution to the oriented Plateau problem for its boundar…
Minimal submanifolds with multiple isolated singularities
Bryan Dimler
We extend Smale's singular bridge principle [Ann. of Math. 130 (1989), 603-642] for -dimensional strictly stable minimal cones in ) to arbitrary co…
Strict stability of calibrated cones
Bryan Dimler, Jooho Lee
We study the strict stability of calibrated cones with an isolated singularity. For special Lagrangian cones and coassociative cones, we prove the strict stability. In the complex…
Partial regularity for Lipschitz solutions to the minimal surface system
Bryan Dimler
In this paper, we study the regularity of several notions of Lipschitz solutions to the minimal surface system with an emphasis on partial regularity results. These include station…