16 dec 2025 -- 11:30   [open in google calendar]

Scuola Normale Superiore, Aula Contini

Please notice the change of room

Abstract.

We present convex integration - type results on the existence and multiplicity of solutions to the isometric immersion system and the closely related Monge-Ampère system (which is an extension of the 2d Monge-Ampère equation arising from the prescribed curvature problem). In particular, we sketch the proof of our most recent result in this context, stating that for any 2d metric $g\in C^{r,\beta}$, an isometric immersion into $R^4$, of regularity $C^{1,\alpha}$ for any $\alpha < \min {1, (r+\beta)/2}$, may be found arbitrarily close to any short immersion.