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1. Geometric Separation in $$\mathbb {R}^3$$ R 3

   https://doi.org/10.1007/s00041-017-9569-z  

   Guo, Kanghui; Labate, Demetrio (January 2018, Journal of Fourier Analysis and Applications)
2. On the nonexistence of automorphic eigenfunctions of exponential growth on SL(3,Z)∖SL(3,R)/SO(3,R)

   https://doi.org/10.1007/s40993-019-0168-8  

   Miller, Stephen D.; Trinh, Tien D. (October 2019, Research in number theory)

   It is well-known that there are automorphic eigenfunctions on SL(2,Z)∖SL(2,R)/SO(2,R)—such as the classical j-function—that have exponential growth and have exponentially growing Fourier coefficients (e.g., negative powers of q=e2πiz, or an I-Bessel function). We show that this phenomenon does not occur on the quotient SL(3,Z)∖SL(3,R)/SO(3,R) and eigenvalues in general position (a removable technical assumption). More precisely, if such an automorphic eigenfunction has at most exponential growth, it cannot have non-decaying Whittaker functions in its Fourier expansion. This confirms part of a conjecture of Miatello and Wallach, who assert all automorphic eigenfunctions on this quotient (among other rank ≥2 examples) always have moderate growth. We additionally confirm their conjecture under certain natural hypotheses, such as the absolute convergence of the eigenfunction’s Fourier expansion. 

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3. Crystallization Retardation of Ultrathin Films of Poly[(R)-3-hydroxybutyrate] and a Random Copolymer Poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyhexanoate] on an Aluminum Oxide Surface,

   https://doi.org/10.1021/acs.macromol.9b01214  

   Liu, Changhao; Noda, Isao; Chase, D. Bruce; Zhang, Yuying; Qu, Jing; Jia, Meng; Ni, Chaoying; Rabolt, John F. (January 2019, Macromolecules)

   null (Ed.)
4. Structure and Growth Habits of Solution-Grown Single Crystals of a Random Copolymer, Poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyhexanoate]

   Liu, Changhou; Noda, Isao; Martin, David; Chase, Bruce D.; Ni, Chao; Rabolt, John F. (October 2018, Polymer)

   Single crystals of a random copolymer, Poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyhexanoate] (PHBHx), with a relatively high (R)-3-hydroxyhexanoate (3HHx) content of 3.9 mol% were grown from dilute solutions over a wide range of crystallization temperatures (Tc) from -20 °C to 75 °C. Unlike Poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyvalerate] (PHBV) which allows the 3-hydroxyvalerate (3HV) to be included into PHB lattice, 3HHx is excluded from the lattice as a non-crystallizable molecular defect. Remarkably, however, even at such a high defect content, all the samples (except for Tc = -20 °C) formed well-developed needle-shaped single crystals, with a crystal morphology similar to that found for crystals of the homopolymer PHB. 

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5. Legendrian contact homology in $$\mathbb{R}^3$$

   https://doi.org/10.4310/SDG.2020.v25.n1.a4  

   Etnyre, John B.; Ng, Lenhard L. (January 2020, Surveys in Differential Geometry)