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1. Period domains for gravitational instantons

   https://doi.org/10.1090/tran/8856  

   Lee, Tsung-Ju; Lin, Yu-Shen (August 2023, Transactions of the American Mathematical Society)

   Based on the uniformization theorems of gravitation instantons by Chen–Chen [Acta Math. 227 (2021), pp. 263–307], Chen–Viaclovsky [Gravitational instantons with quadratic volume growth, 2021], Collins–Jacob–Lin [Forum Math. Sigma (2021)], and Hein–Sun–Viaclovsky–Zhang [Gravitational instantons and del Pezzo surfaces], we prove that the period maps for the ${\mathrm{A}\mathrm{L}\mathrm{H}}^{\ast <\#comment/>}$, $\mathrm{A}\mathrm{L}\mathrm{G}$, and ${\mathrm{A}\mathrm{L}\mathrm{G}}^{\ast <\#comment/>}$gravitational instantons are surjective. In particular, the period domains of these gravitational instantons are exactly their moduli spaces. 

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2. Gravitational instantons with quadratic volume growth

   https://doi.org/10.1112/jlms.12886  

   Chen, Gao; Viaclovsky, Jeff (March 2024, Journal of the London Mathematical Society)

   Abstract There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type and . Gravitational instantons of type were previously classified by Chen–Chen. In this paper, we prove a classification theorem for gravitational instantons. We determine the topology and prove existence of “uniform” coordinates at infinity for both ALG and gravitational instantons. We also prove a result regarding the relationship between ALG gravitational instantons of order and those of order 2. 

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3. Pathways to Detection of Strongly-Bound Inorganic Species: The Vibrational and Rotational Spectral Data of AlH2OH, HMgOH, AlH2NH2, and HMgNH2

   https://doi.org/10.3389/fspas.2021.643348  

   Watrous, Alexandria G.; Davis, Megan C.; Fortenberry, Ryan C. (March 2021, Frontiers in Astronomy and Space Sciences)

   Small, inorganic hydrides are likely hiding in plain sight, waiting to be detected toward various astronomical objects. AlH 2 OH can form in the gas phase via a downhill pathway, and the present, high-level quantum chemical study shows that this molecule exhibits bright infrared features for anharmonic fundamentals in regions above and below that associated with polycyclic aromatic hydrocarbons. AlH 2 OH along with HMgOH, HMgNH 2 , and AlH 2 NH 2 are also polar with AlH 2 OH having a 1.22 D dipole moment. AlH 2 OH and likely HMgOH have nearly unhindered motion of the hydroxyl group but are still strongly bonded. This could assist in gas phase synthesis, where aluminum oxide and magnesium oxide minerals likely begin their formation stages with AlH 2 OH and HMgOH. This work provides the spectral data necessary to classify these molecules such that observations as to the buildup of nanoclusters from small molecules can possibly be confirmed. 

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4. Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry

   https://doi.org/10.1093/imrn/rnae200  

   Biquard, Olivier; Gauduchon, Paul; LeBrun, Claude (September 2024, International Mathematics Research Notices)

   Abstract In a previous paper [7], the first two authors classified complete Ricci-flat ALF Riemannian 4-manifolds that are toric and Hermitian, but non-Kähler. In this article, we consider general Ricci-flat metrics on these spaces that are close to a given such gravitational instanton with respect to a norm that imposes reasonable fall-off conditions at infinity. We prove that any such Ricci-flat perturbation is necessarily Hermitian and carries a bounded, non-trivial Killing vector field. With mild additional hypotheses, we are then able to show that the new Ricci-flat metric must actually be one of the known gravitational instantons classified in [7]. 

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5. Scalar curvature deformation and mass rigidity for ALH manifolds with boundary

   https://doi.org/10.1090/tran/8755  

   Huang, Lan-Hsuan; Jang, Hyun Chul (November 2022, Transactions of the American Mathematical Society)

   We study scalar curvature deformation for asymptotically locally hyperbolic (ALH) manifolds with nonempty compact boundary. We show that the scalar curvature map is locally surjective among either (1) the space of metrics that coincide exponentially toward the boundary, or (2) the space of metrics with arbitrarily prescribed nearby Bartnik boundary data. Using those results, we characterize the ALH manifolds that minimize the Wang-Chruściel-Herzlich mass integrals in great generality and establish the rigidity of the positive mass theorems. 

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