Jonas Hirsch

activity

20232026

collaborators

4 papers

math.AP2026

Full flexibility of the Monge-Ampère system in codimension $d_{*} - d + 1$

Wentao Cao, Jonas Hirsch, Dominik Inauen +1

We prove that $C^{1, α}$ 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 spac…

math.AP2025

Isometric Immersions and Weak Solutions to the Darboux Equation

Wentao Cao, Jonas Hirsch, Dominik Inauen

We study the Darboux equation, a fundamental PDE arising in the theory of isometric immersions of two-dimensional Riemannian manifolds into $R^{3}$ , in the low-regularity re…

math.AP2025

A Nash-Kuiper theorem for isometric immersions beyond Borisov's exponent

Wentao Cao, Jonas Hirsch, Dominik Inauen

Given any short immersion from an $n$ -dimensional bounded and simply connected domain into $R^{n + 1}$ and any Hölder exponent $α < (1 + n^{2} - n)^{- 1}$ , we construct a $C^{1, α}$ …

math.AP2023

$C^{1, \frac{1}{3} -}$ very weak solutions to the two dimensional Monge-Ampére equation

Wentao Cao, Jonas Hirsch, Dominik Inauen

For any $θ < \frac{1}{3}$ , we show that very weak solutions to the two-dimensional Monge-Ampère equation with regularity $C^{1, θ}$ are dense in the space of continuous functions. Thi…

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

Isometric Immersions and Weak Solutions to the Darboux Equation

A Nash-Kuiper theorem for isometric immersions beyond Borisov's exponent

C1,31​− very weak solutions to the two dimensional Monge-Ampére equation

Full flexibility of the Monge-Ampère system in codimension $d_{*} - d + 1$

$C^{1, \frac{1}{3} -}$ very weak solutions to the two dimensional Monge-Ampére equation