@article{LiebThirring1975,
  author = {Lieb, Elliott H. and Thirring, Walter E.},
  title = {Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter},
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  pages = {687--689},
  year = {1975},
  doi = {10.1103/PhysRevLett.35.687},
  note = {Erratum, ibid. 35 (1975), 1116}
}

@incollection{LiebThirring1976,
  author = {Lieb, Elliott H. and Thirring, Walter E.},
  title = {Inequalities for the Moments of the Eigenvalues of the {Schr\"odinger} {Hamiltonian} and Their Relation to {Sobolev} Inequalities},
  booktitle = {Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann},
  editor = {Lieb, Elliott H. and Simon, Barry and Wightman, Arthur S.},
  publisher = {Princeton University Press},
  address = {Princeton, NJ},
  pages = {269--303},
  year = {1976}
}

@article{Keller1961,
  author = {Keller, Joseph B.},
  title = {Lower Bounds and Isoperimetric Inequalities for Eigenvalues of the {Schr\"odinger} Equation},
  journal = {Journal of Mathematical Physics},
  volume = {2},
  number = {2},
  pages = {262--266},
  year = {1961},
  doi = {10.1063/1.1703708}
}

@article{AizenmanLieb1978,
  author = {Aizenman, Michael and Lieb, Elliott H.},
  title = {On Semi-Classical Bounds for Eigenvalues of {Schr\"odinger} Operators},
  journal = {Physics Letters A},
  volume = {66},
  number = {6},
  pages = {427--429},
  year = {1978},
  doi = {10.1016/0375-9601(78)90385-7}
}

@article{HundertmarkLiebThomas1998,
  author = {Hundertmark, Dirk and Lieb, Elliott H. and Thomas, Lawrence E.},
  title = {A Sharp Bound for an Eigenvalue Moment of the One-Dimensional {Schr\"odinger} Operator},
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  doi = {10.4310/ATMP.1998.v2.n4.a2},
  eprint = {math-ph/9806012},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math-ph/9806012v2}
}

@article{LaptevWeidl2000,
  author = {Laptev, Ari and Weidl, Timo},
  title = {Sharp {Lieb--Thirring} Inequalities in High Dimensions},
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  archivePrefix = {arXiv},
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}

@misc{ReadSchulz2026,
  author = {Read, Larry and Schulz, Marvin R.},
  title = {The Sharp One-Dimensional {Lieb--Thirring} Inequality for the Sum of Eigenvalues},
  year = {2026},
  eprint = {2609.10478v2},
  archivePrefix = {arXiv},
  primaryClass = {math.SP},
  howpublished = {\href{https://arxiv.org/abs/2609.10478v2}{arXiv:2609.10478v2}},
  note = {Version 2, 14 September 2026},
  url = {https://arxiv.org/abs/2609.10478v2}
}

@book{Teschl2009,
  author = {Teschl, Gerald},
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  publisher = {American Mathematical Society},
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}

@article{Hiai2010,
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}

@book{Milnor1965,
  author = {Milnor, John W.},
  title = {Topology from the Differentiable Viewpoint},
  publisher = {University Press of Virginia},
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}

@article{Weidl1996,
  author = {Weidl, Timo},
  title = {On the {Lieb--Thirring} constants {$L_{\gamma,1}$} for {$\gamma\geq1/2$}},
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@article{HLW2000,
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}

@article{EdenFoias1991,
  author = {Eden, A. and Foias, Ciprian},
  title = {A simple proof of the generalized {Lieb--Thirring} inequalities in one-space dimension},
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@article{DLL2008,
  author = {Dolbeault, Jean and Laptev, Ari and Loss, Michael},
  title = {{Lieb--Thirring} inequalities with improved constants},
  journal = {Journal of the European Mathematical Society},
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}

@article{FHJN2021,
  author = {Frank, Rupert L. and Hundertmark, Dirk and Jex, Michal and Nam, Phan Th{\`a}nh},
  title = {The {Lieb--Thirring} inequality revisited},
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@article{CorsoRied2025,
  author = {Corso, Thiago Carvalho and Ried, Tobias},
  title = {On a variational problem related to the {Cwikel--Lieb--Rozenblum} and {Lieb--Thirring} inequalities},
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@article{Levitt2014,
  author = {Levitt, Antoine},
  title = {Best constants in {Lieb--Thirring} inequalities: a numerical investigation},
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}

@article{BuslaevFaddeev1960,
  author = {Buslaev, Vladimir S. and Faddeev, Ludvig D.},
  title = {Formulas for traces for a singular {Sturm--Liouville} differential operator},
  journal = {Doklady Akademii Nauk SSSR},
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@article{ZakharovFaddeev1971,
  author = {Zakharov, Vladimir E. and Faddeev, Ludvig D.},
  title = {{Korteweg--de Vries} equation: A completely integrable {Hamiltonian} system},
  journal = {Functional Analysis and Its Applications},
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  number = {4},
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  year = {1971},
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@article{GardnerGreeneKruskalMiura1974,
  author = {Gardner, Clifford S. and Greene, John M. and Kruskal, Martin D. and Miura, Robert M.},
  title = {{Korteweg--de Vries} equation and generalizations. {VI}. {Methods} for exact solution},
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  year = {1974},
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@incollection{BenguriaLoss2004,
  author = {Benguria, Rafael D. and Loss, Michael},
  title = {Connection between the {Lieb--Thirring} conjecture for {Schr\"odinger} operators and an isoperimetric problem for ovals on the plane},
  booktitle = {Partial Differential Equations and Inverse Problems},
  series = {Contemporary Mathematics},
  volume = {362},
  pages = {53--61},
  publisher = {American Mathematical Society},
  year = {2004},
  doi = {10.1090/conm/362/06604},
  eprint = {math-ph/0402048},
  archivePrefix = {arXiv}
}

@incollection{DaleckiiKrein1965,
  author = {Daleckii, Ju. L. and Krein, S. G.},
  title = {Integration and differentiation of functions of {Hermitian} operators and applications to the theory of perturbations},
  booktitle = {American Mathematical Society Translations, Series 2},
  volume = {47},
  pages = {1--30},
  publisher = {American Mathematical Society},
  year = {1965},
  doi = {10.1090/trans2/047/01}
}

@article{Petz1994,
  author = {Petz, D{\'e}nes},
  title = {A survey of certain trace inequalities},
  journal = {Banach Center Publications},
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  pages = {287--298},
  year = {1994},
  doi = {10.4064/-30-1-287-298}
}