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John McCuan : Minimal graphs with jump discontinuities

I will discuss some examples of minimal graphs with jump discontinuities in their boundaries. Robert Huff and I constructed these examples in response to a question of John Urbas: Is it possible for a minimal graph over a smooth annular domain to have an isolated jump discontinuity on the inner boundary component? I will also give a brief overview of the boundary consistency problem for Di Giorgi's generalized solutions of the minimal surface equation and discuss this question in that context. The construction of the examples uses the Weierstrass representation and the developing map introduced by Huff in the study of capillary problems.

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