| Abstract: |
| The special Lagrangian equation is the potential equation for volume-minimizing Lagrangian graphs. Good regularity results are available when the Lagrangian phase is large, which corresponds to the equation being concave. On the other hand, little is known when the phase is small. For example, it is open whether interior gradient estimates hold in the case of small phase. We will discuss some results which are steps towards answering this question, including a rigidity result that rules out counterexamples with homogeneous structure, and an interior gradient estimate for large variable phase. The latter is joint work with A. Bhattacharya and R. Shankar. |
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