Author

S. Shi

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Preprint Sep 2026

Lewy-Type Nondegeneracy for Gradient-Dependent Elliptic Equations and Global Gradient Diffeomorphisms on Convex Rings

We prove two complementary Lewy-type theorems for elliptic equations whose coefficients depend only on the gradient. First, let $\Omega\subset\mathbb{R}^3$ and let $u$ solve \[ a^{ij}(Du)u_{ij}=0, \] where $a$ is a smooth, symmetric, positive definite matrix field on an open set containing $Du(\Omega)$. We show that if...

Da Liu, Shu-Jun Shi · 0 citations

Preprint Sep 2026

Universal Spacelikeness Estimates and Liouville Rigidity for Lorentzian $\sigma_k$ Curvature Equations

We study nonnegative entire spacelike graphs in Lorentz--Minkowski space satisfying $\sigma_k(A[u])=u^p$. For $2\le k<n$ and $p\ge k$, pointwise strict spacelikeness and closed $k$-admissibility yield universal bounds for the height and Lorentz factor. Their proof combines block coercivity in the full G\r{a}rding cone,...

Shu-Jun Shi, Yuzhou Zhang · 0 citations

Preprint Sep 2026

Universal Spacelikeness Estimates and Liouville Rigidity for Lorentzian $\sigma_k$ Curvature Equations

We study nonnegative entire spacelike graphs in Lorentz--Minkowski space satisfying $\sigma_k(A[u])=u^p$, with $h_{ij}=-Wu_{ij}$ and $W=(1-|Du|^2)^{-1/2}$. For $2\leq k<n$ and $p\geq k$, we establish bounds for the height and the Lorentz factor that depend only on $n,k,p$, assuming pointwise strict spacelikeness and ad...

S. Shi, Yuzhou Zhang · 0 citations