Jian-Ping Sun | Search arXiv

arXiv2026

The solvability of the $L_p$-dual mixed Euclidean-Gauss Minkowski problem

This paper investigates the $L_p$-dual mixed Euclidean-Gauss Minkowski problem associated with the $L_p$-dual mixed Euclidean-Gaussian curvature measure. The solvability of this problem is equivalent to that of a class of Monge-Ampère type equations on the unit sphere. Under smooth assumptions, We establish the existence of solutions for $p<1$, $q<0$, and $q<p$ and uniqueness of solutions for $p\geq q$ to the aforementioned Monge-Ampère type equations, respectively. Furthermore, we obtain a complete solution concerning the existence part of this problem when $p<1$ and $q<0$.

math.AP↗

arXiv2026

Polar, checkerboard charge order in bilayer nickelate La3Ni2O7

Competing charge and spin orders are central to uncovering the nature of unconventional superconductivity. Here we utilize synchrotron X-ray diffraction on a high-quality single crystal to reveal the charge order of La$_3$Ni$_2$O$_7$ at ambient pressure, which competes with the high-temperature superconducting phase under pressure. Enabled by the high synchrotron photon flux and a large dynamic range, we resolve faint reflections -- nearly four orders of magnitude weaker than the main Bragg reflections -- that were overlooked in prior diffraction studies. This observation evidences a broken glide-mirror symmetry, leading to a polar crystal structure, rather than the widely used centrosymmetric structure model. The polarity is induced by checkerboard charge order on nickel sites in combination with octahedral tilting, reminiscent of bilayer manganese oxides. Our results provide a foundation for understanding phase competition and the mechanism of pressure-induced superconductivity in bilayer nickelates.

cond-mat.supr-con↗