3 papers
math.AP2026
The Extra Vanishing Structure and Nonlinear Stability of Multi-Dimensional Rarefaction Waves: The Geometric Weighted Energy Estimates
Haoran He, Qichen He
We study the resolution of discontinuous singularities in gas dynamics via multi-dimensional rarefaction waves. While the mechanism is well-understood in one spatial dimension, the…
math.FA2026
A Fubini Theorem for Grothendieck Functional Integrals
Haoran He, Qichen He
This paper systematically studies the subset of continuous linear functionals on the projective tensor product of Banach spaces whose norms are bounded by Grothendieck's constant $…
math.DG2026
The Coupled Hitchin-He Equations: Integrable Deformations and Rigidity of the Moduli Space
Haoran He, Qichen He
We introduce the \emph{parameter-geometrization} to the Hitchin system, a paradigm embedding deformation parameters into geometry via the coupled Hitchin-He equations on a surface…