Wentao Cao

collaborators

4 papers

math.AP2026

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

Wentao Cao, Jonas Hirsch, Dominik Inauen +1

We prove that $C^{1, I^\pm}$ solutions to the Monge-AmpÃ¨re system in dimension $d$ and codimension $k = d_{*} - d + 1$ , where $d_{*}$ denotes the Janet dimension, are dense in the sp…

math.AP2025

Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation

Wentao Cao, Zhehui Wang

We investigate the Dirichlet problem of the two dimensional Lagrangian mean curvature equation in a bounded domain. Infinitely many $C^{1, I^\pm} (I^\pm \in (0, \frac{1}{5}))$ very weak so…

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 HÃ¶lder exponent $I^\pm < (1 + n^{2} - n)^{- 1}$ , we construct a $C^{1, Î±…

Full flexibility of the Monge-AmpÃ¨re system in codimension d∗​−d+1

Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation

Isometric Immersions and Weak Solutions to the Darboux Equation

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

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