Dominik Inauen

activity

20152026

most citedRigidity and Flexibility of Isometric Extensions

5 citations · 7 across the 11 of their papers we have counts for

collaborators

12 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

The Monge-Ampère system in dimension two is fully flexible in codimension two

Dominik Inauen, Marta Lewicka

We prove that every $C^{1} (ω ˉ)$ -regular subsolution of the Monge-Ampère system posed on a $2$ -dimensional domain $ω$ and with target codimension $2$ , can be uniformly ap…

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.AP2025

The Monge-Ampere system in dimension two and codimension three

Dominik Inauen, Marta Lewicka

We revisit the convex integration constructions for the Monge-Ampère system and prove its flexibility in dimension $d = 2$ and codimension $k = 3$ , up to $C^{1, 1 - 1/ 5}$ …

math.PR2023

Stochastic Nash evolution

Dominik Inauen, Govind Menon

This paper introduces a probabilistic formulation for the isometric embedding of a Riemannian manifold $(M^{n}, g)$ into Euclidean space $R^{q}$ . Given $α \in] \frac{1}{2}, 1]$ ,…

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…

math.PR2022

Dyson Brownian Motion and motion by mean curvature

Ching-Peng Huang, Dominik Inauen, Govind Menon

We construct Dyson Brownian motion for $β \in (0, \infty]$ by adapting the extrinsic construction of Brownian motion on Riemannian manifolds to the geometry of group orbits within th…

math.AP2020★ 5 cited

Rigidity and Flexibility of Isometric Extensions

Wentao Cao, Dominik Inauen

In this paper we consider the rigidity and flexibility of $C^{1, θ}$ isometric extensions and we show that the Hölder exponent $θ_{0} = \frac{1}{2}$ is critical in the following sense: if…

math.AP2018★ 1 cited

$C^{1, α}$ Isometric Embeddings of Polar Caps

Camillo De Lellis, Dominik Inauen

We study isometric embeddings of $C^{2}$ Riemannian manifolds in the Euclidean space and we establish that the Hölder space $C^{1, \frac{1}{2}}$ is critical in a suitable sense: in pa…

math.CA2017

Fractional Sobolev Regularity for the Brouwer Degree

Camillo De Lellis, Dominik Inauen

We prove that if $Ω \subset R^{n}$ is a bounded open set and $n α > dim_{b} (\partial Ω) = d$ , then the Brouwer degree deg $(v, Ω, \cdot)$ of any Hölder function $v\in C^{0,α}\…

math.DG2015★ 1 cited

A Nash-Kuiper theorem for $C^{1, \frac{1}{5} - δ}$ immersions of surfaces in $3$ dimensions

Camillo De Lellis, Dominik Inauen, László Székelyhidi

We prove that, given a $C^{2}$ Riemannian metric $g$ on the $2$ -dimensional disk $D_{2}$ , any short $C^{1}$ immersion of $(D_{2}, g)$ into $R^{3}$ can be uniformly approximated with $…

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

Isometric Immersions and Weak Solutions to the Darboux Equation

The Monge-Ampère system in dimension two is fully flexible in codimension two

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

The Monge-Ampere system in dimension two and codimension three

Stochastic Nash evolution

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

Dyson Brownian Motion and motion by mean curvature

Rigidity and Flexibility of Isometric Extensions

C1,α Isometric Embeddings of Polar Caps

Fractional Sobolev Regularity for the Brouwer Degree

A Nash-Kuiper theorem for C1,51​−δ immersions of surfaces in 3 dimensions

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

$C^{1, α}$ Isometric Embeddings of Polar Caps

A Nash-Kuiper theorem for $C^{1, \frac{1}{5} - δ}$ immersions of surfaces in $3$ dimensions