Geometric mechanics on product Heisenberg groups

References

• Beals , R , Gaveau , B and Greiner , PC . 1997 . Complex Hamiltonian mechanics and parametrices for subelliptic Laplacians, I, II, III . Bull. Sci. Math. , 21 : 1 – 36 . 97–149, 195–259
   Google Scholar
• Beals , R , Gaveau , B and Greiner , PC . 2000 . Hamilton–Jacobi theory and the heat kernel on the Heisenberg groups . J. Math. Pure Appl. , 79 ( #7 ) : 633 – 689 .
   Google Scholar
• Beals , R and Greiner , PC . 1988 . Calculus on Heisenberg Manifolds, Annals of Mathematics Studies , Vol. 119 , Princeton, NJ : Princeton University Press .
   Google Scholar
• Calin , O , Chang , DC and Greiner , P . 2007 . Geometric Analysis on the Heisenberg Group and its Generalizations , Cambridge, MA : AMS/IP Series in Advanced Mathematics, #40, International Press .
   Google Scholar
• Folland , GB and Stein , EM . 1974 . Estimates for the complex and analysis on the Heisenberg group . Comm. Pure Appl. Math. , 27 : 429 – 522 .
   Web of Science ®Google Scholar
• Calin , O , Chang , DC and Greiner , P . 2005 . Geometric analysis on the Heisenberg group . Bull. Acad. Sinica , 33 ( #3 ) : 185 – 252 .
   Google Scholar
• Chang , DC and Greiner. , P . 2004 . “ Analysis and geometry on Heisenberg groups ” . In Proceedings of Second International Congress of Chinese Mathematicians. , Edited by: Lin , C and Yau , ST . 379 – 405 . New Studies in Advanced Mathematics, International Press .
   Google Scholar
• Chang , DC and Greiner , P . 2008 . “ Subelliptic PDEs and sub-Riemannian geometry ” . In Proceedings of Third International Congress of Chinese Mathematicians , 223 – 237 . Cambridge, MA : AMS/IP Studies in Advanced Mathematics, 42, International Press .
   Google Scholar
• D.C. Chang and P. Greiner, Fundamental solutions for Kohn Laplacians on a family of pseudoconvex hypersurfaces, 2007, in Proceedings of the 4th International Congress of Chinese Mathematicians, to be published by International Press, Cambridge, MA, 2009
   Google Scholar
• Chang , DC , Markina , I and Vasilév , A . 2008 . Sub-Lorentzian geometry on Anti-De Sitter space . J. Math. Pures Appl. , 90 : 82 – 110 .
   Google Scholar
• Berenstein , C , Chang , DC and Tie , J . 2001 . Laguerre Calculus and its Applications in the Heisenberg Group , Cambridge, MA : AMS/IP series in Advanced Mathematics, #22, International Press .
   Google Scholar
• Chang , DC and Tie , J . 2000 . Estimates for powers of sub-Laplacian on the non-isotropic Heisenberg group . J. Geom. Anal. , 10 : 653 – 678 .
   Google Scholar
• Chow , WL . 1939 . Uber systeme von linearen partiellen differentialgleichungen erster ordnung . Math. Ann. , 117 : 98 – 105 .
   Google Scholar
• Rashevskiĭ , PK . 1938 . About connecting two points of complete nonholonomic space by admissible curve . Uch. Zapiski Ped. Inst. K. Liebknecht , 2 : 83 – 94 .
   Google Scholar
• Hörmander , L . 1967 . Hypoelliptic second-order differential equations . Acta Math. , 119 : 147 – 171 .
   Web of Science ®Google Scholar
• Calin , O , Chang , DC and Markina , I . 2009 . “ Generalized Hamilton–Jacoby equation and heat kernel on step two nilpotent Lie groups ” . In Analysis and Mathematical Physics, in Proceedings of the conference ‘New trends in harmonic and complex analysis’ , Edited by: Vasiliev , A and Markina , I . Vol. 2007 , Birchauser-Verlag : Voss .
   Google Scholar
• Gaveau , B . 1977 . Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents . Acta Math. , 139 ( #1–2 ) : 95 – 153 .
   Google Scholar
• P. Greiner, On Hömander operators and non-holonomic geometry, in Pseudo-differential operators: partial differential equations and time-frequency analysis, Fields Institute Communications, 52, American Mathematical Society, M.W. Wong, ed., Providence, RI, pp. 1–25, 2007
   Google Scholar
• Iacob , C , Homentcovschi , D , Marcov , N and Nicolau , A . 1983 . Matematici Clasice si Moderne , Bucuresti : Ed. Tehnica .
   Google Scholar