Jonas Hirsch

Full flexibility of the Monge-Ampère system in codimension d∗ − d + 1

We prove that $\mathcal{C}^{1,α}$ solutions to the Monge-Ampère system in dimension $d$ and codimension $k= d_*-d+1$, where $d_*$ denotes the Janet dimension, are dense in the space of continuous functions, for every Hölder exponent $α<1$. Our result strengthens the statement in...

On the Lawson-Osserman conjecture

Abstract We prove that if $u : B_{1} \subset \mathbb{R}^{2} \rightarrow \mathbb{R}^{n}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>u</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>⊂</mml:mo> <mml:msup> <mml:...