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1. Bi-Sobolev Extensions

   https://doi.org/10.1007/s12220-023-01363-1  

   Koski, Aleksis; Onninen, Jani (July 2023, The Journal of Geometric Analysis)

   Abstract We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal variant of the famous Beurling–Ahlfors extension theorem is obtained. Furthermore we show that the existing extension techniques such as applying either the harmonic or the Beurling–Ahlfors operator work poorly in the degenerated setting. This also gives an affirmative answer to a question of Karafyllia and Ntalampekos. 

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2. Bi-incomplete Tambara functors

   Blumberg, Andrew J; Hill, Michael A. (January 2022, London Mathematical Society lecture note series)
3. Bi-incomplete Tambara functors

   Blumberg, Andrew J.; Hill, Michael A. (January 2021, Equivariant Topology and Derived Algebra)

   Balchin, S.; Barnes, D.; Kędziorek, M.; Szymik, M. (Ed.)

   For an equivariant commutative ring spectrum R, \pi_0 R has algebraic structure reflecting the presence of both additive transfers and multiplicative norms. The additive structure gives rise to a Mackey functor and the multiplicative structure yields the additional structure of a Tambara functor. If R is an N_\infty ring spectrum in the category of genuine G-spectra, then all possible additive transfers are present and \pi_0 R has the structure of an incomplete Tambara functor. However, if R is an N_\infty ring spectrum in a category of incomplete G-spectra, the situation is more subtle. In this chapter, we study the algebraic theory of Tambara structures on incomplete Mackey functors, which we call bi-incomplete Tambara functors. Just as incomplete Tambara functors have compatibility conditions that control which systems of norms are possible, bi-incomplete Tambara functors have algebraic constraints arising from the possible interactions of transfers and norms. We give a complete description of the possible interactions between the additive and multiplicative structures. 

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4. Bi-Sobolev boundary singularities

   https://doi.org/10.1007/s40627-023-00114-w  

   Iwaniec, Tadeusz; Onninen, Jani; Zhu, Zheng (March 2023, Complex Analysis and its Synergies)
5. Analyzing the bi-directional dynamic morphing of a bi-stable water-bomb base origami

   https://doi.org/10.1117/12.2512301  

   Sadeghi, Sahand and (March 2019, Proceedings of SPIE Smart Structures + Nondestructive Evaluation, 2019 Denver, CO, United States)