Lecture Notes

• J. Weber
  Introduction to Sobolev spaces
  Preliminary version, 23 December 2018
    
  

In preparation

• J. Weber
  Lecture Notes on Morse and Conley theory
  In progress
  
  
• J. Weber
  The heat flow and the homology of the loop space
  Book in preparation
  
  
• J. Weber
  Global stable foliations for the heat flow
  In preparation
  

Publications

Books

• J. Weber
  Topological Methods in the Quest for Periodic Orbits
  Extended version contracted by the EMS for their EMS Series of Lectures in Mathematics
  
  
• J. Weber
  Scale Calculus and M-Polyfolds - An Introduction 
  32o Colóquio Brasileiro de Matemática, CBM-32, IMPA (2019), iii+138 pages.
  ISBN 978-85-244-0428-3
  download book here or here
  
  
• J. Weber
  Topological Methods in the Quest for Periodic Orbits
  31o Colóquio Brasileiro de Matemática, CBM-31, IMPA (2017), vii+248 pages.
  ISBN 978-85-244-0439-9
  download book here or here
  

Translations

• W. Weber
  Electrodynamic Measurements, especially on the Energy of Interaction 
  Translator from German to English: J. Weber
  article (2020), 64 pages, included as Chapter 13 in this book (2021).
  
  
• D.A. Salamon
  Análise em dimensões superiores
  Tradutor do alemão ao português: J. Weber
  livro (2019), ix+376 páginas.
  

Papers

• U. Frauenfelder and J. Weber
  Local gluing
  Preprint, 45 pages
  viXra:2401.0075 science, freedom, dignity 
    
   
  
• U. Frauenfelder and J. Weber
  Lagrange multipliers and adiabatic limits I
  Preprint, 60 pages
  viXra:2210.0061 science, freedom, dignity 
  
  
• U. Frauenfelder and J. Weber
  Lagrange multipliers and adiabatic limits II
  Preprint, 47 pages 
  viXra:2210.0057 science, freedom, dignity 
  
  
• U. Frauenfelder and J. Weber
  A mathematical description of the Weber nucleus as a classical and quantum mechanical system
  Anal. Math. Phys. 14, 31 (2024), 1-26.
  doi: 10.1007/s13324-024-00891-5 open access  SharedIt  viXra:2207.0070 science, freedom, dignity. 
  arXiv 🤐 deleted submission overnight: allegedly beeing not even "refereeable for publication in a conventional journal". Not refereeable - professional engineering.
  
  
• U. Frauenfelder and J. Weber
  The regularized free fall II - Homology computation via heat flow
  Topol. Methods Nonlinear Anal. 60 no.1 (2022), 343-361. 
  doi: 10.12775/TMNA.2021.060 '??' cf. proofs  links Ok   arXiv:2107.12175
  
  
• U. Frauenfelder and J. Weber
  The regularized free fall I - Index computations   
  Russian Journal of Mathematical Physics 28 no.4 (2021), 464-487.  RJMP
  doi: 10.1134/S1061920821040063   SharedIt   arXiv:2102.01688
  
  
• U. Frauenfelder and J. Weber
  The shift map on Floer trajectory spaces
  J. Symplectic Geom. 19 no.2 (2021), 351-397.
  doi: 10.4310/JSG.2021.v19.n2.a2   arXiv:1803.03826
  
  
• U. Frauenfelder and J. Weber
  The fine structure of Weber's hydrogen atom - Bohr-Sommerfeld approach
  Zeitschrift für angewandte Mathematik und Physik 70 no.4 (2019), 105-116.  
  doi: 10.1007/s00033-019-1149-4   SharedIt   arXiv:1902.09612  🤐
  
  
• J. Weber
  Conley pairs in geometry - Lusternik-Schnirelmann theory and more
  Expo. Math. 37 no.1 (2019), 25-47.
  doi: 10.1016/j.exmath.2017.10.003   arXiv:1709.05010
  
  
• J. Weber
  Stable foliations and semi-flow Morse homology
  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XVII no.3 (2017), 853-909.
  doi: 10.2422/2036-2145.201510_017   arXiv:1408.3842
  
  
• J. Weber
  Classical Morse theory revisited I - Backward λ-Lemma and homotopy type
  Topol. Methods Nonlinear Anal. 47 no.2 (2016), 641-646.
  doi: 10.12775/⁠TMNA.2016.020   arXiv:1410.0995
  
  
• J. Weber
  Contraction method and Lambda-Lemma
  São Paulo J. Math. Sci. 9 no.2 (2015), 263-298.
  doi: 10.1007/s40863-015-0014-4   arXiv:1507.01028
  
  
• J. Weber
  The Backward λ-Lemma and Morse Filtrations
  Progress in Nonlinear Differential Equations and Their Applications 85 (2014), 457-466.
  doi: 10.1007/978-3-319-04214-5_27   book   arXiv:1211.2180
  
  
• J. Weber
  A backward λ-Lemma for the forward heat flow
  Math. Ann. 359 no.3 (2014), 929-967.
  doi: 10.1007/s00208-014-1026-6   arXiv:1210.3897
  
  
• J. Weber
  Morse homology for the heat flow
  Math. Z. 275 no.1 (2013), 1-54.
  doi: 10.1007/s00209-012-1121-x   Preprint, IME USP, Nov. 2011   cf. arXiv:1003.4350
  

• J. Weber
  Morse homology for the heat flow -- Linear theory
  Math. Nachr. 286 no.1 (2013), 88-104.
  doi: 10.1002/mana.201100319   Preprint, IME USP, Nov. 2011
  
  
• P. Salomão and J. Weber
  An almost existence theorem for non-contractible periodic orbits in cotangent bundles
  São Paulo J. Math. Sci. 6 no.2 (2012), 385-94.
  doi: 10.11606/issn.2316-9028.v6i2p385-394   Article   arXiv:1302.7282
  
  
• J. Weber
  The heat flow and the homology of the loop space
  Habilitationsschrift, HU Berlin, 08 February 2010, 1-139.
  Habilitation monograph
  
  
• J. Weber
  A product estimate, the parabolic Weyl lemma and applications
  Preprint, HU Berlin, Sep. 2009   arXiv:0910.2739
  
  
• J. Weber
  Noncontractible periodic orbits in cotangent bundles and Floer homology
  Duke Math. J. 133 no.3 (2006), 527-568.
  doi: 10.1215/S0012-7094-06-13334-3   Preprint, ETHZ, Apr. 2004, revised Oct. 2005   math.SG/0410609
  
  
• D. Salamon and J. Weber
  Floer homology and the heat  flow
  GAFA 16 no.5 (2006), 1050-1138.
  doi: 10.1007/s00039-006-0577-4   Preprint, ETHZ, Apr. 2003, revised Oct. 2005   math.SG/0304383  
  
  
• J. Weber
  The Morse-Witten complex via dynamical systems
  Expo. Math. 24 (2006), 127-159.
  doi: 10.1016/j.exmath.2005.09.001   Preprint, Univ. München, Nov. 2004, revised Oct. 2005   math.GT/0411465  
  
  
• J. Weber
  Three approaches towards Floer homology of cotangent bundles
  J. Symplectic Geom. 3 no.4 (2005), 671-701.    
  doi: 10.4310/JSG.2005.v3.n4.a7   Preprint, Univ. München, Feb. 2005, revised Jan. 2006   math.SG/0602230
  
  
• J. Weber
  Noncontractible periodic orbits in cotangent bundles
  Oberwolfach Rep. 2 no.3 (2005), 1787-1789.
  doi: EMS   published report
  
  
• J. Weber
  Perturbed closed geodesics are periodic orbits: Index and Transversality
  Math. Z. 241 no.1 (2002), 45-81
  doi:10.1007/s002090100406   Preprint, ETHZ, May 2001   math.SG/0105153
  
  
• J. Weber
  J-holomorphic curves in cotangent bundles and the heat flow
  Dissertation (PhD thesis), TU Berlin, 1999, 1-215.
  
  
• J. Weber
  Morse-Ungleichungen, Supersymmetrie, und quasiklassischer Limes
  Diplomarbeit (Master's thesis), Fachbereich Physik, TU Berlin, 1995, 1-105.
  
  
• J. Weber
  Der Morse-Witten Komplex
  Diplomarbeit (Master's thesis), Fachbereich Mathematik, TU Berlin, 1993, 1-111.