Intrinsic regular hypersurfaces in Heisenberg groups
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ambrosio, L. Some fine properties of sets of finite perimeter in Ahlfors regular metrice measure spaces,Adv. in Math. 159, 51–67, (2001).
Ambrosio, L., Fusco, N., and Pallara, D.Functions of Bounded Variation and Free Discontinuity Problems, Oxford Science Publications, Oxford (2000).
Ambrosio, L. and Kirchheim, B. Rectifiable sets in metric and Banach spaces,Math. Ann. 318, 527–555, (2000).
Balogh, Z. Size of characteristic sets and functions with prescribed gradient,J. Reine Angew Math. 564, 63–83, (2003).
Balogh, Z., Hofer-Isenegger, H., and Tyson, J. T. Lifts of Lipischitz maps and horizontal fractals in the Heisenberg group, preprint, (2003).
Balogh, Z., Rickly, M., and Serra Cassano, F. Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric,Publ. Math. 47, 237–259, (2003).
Bellaïche, A. The tangent space in subriemannian geometry, inSubriemannian Geometry, Progress in Mathematics,144, Bellaïche, A. and Risler, J., Eds., Birkhäuser Verlag, Basel, (1996).
Biroli, M. and Mosco, U. Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces,Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 6, 37–44, (1995).
Capogna, L., Danielli, D., and Garofalo, N. The geometric Sobolev embedding for vector fields and the isoperimetric inequality,Comm. Anal. Geom. 12, 203–215, (1994).
Citti, G. and Manfredini, M. Dini Theorem in nonhomogeneous Carnot spaces, preprint, (2004).
Cole, D. R. and Pauls, S. C1, 1 hypersurfaces of the Heisenberg group are N-rectifiable, preprint, (2004).
Danielli, D., Garofalo, N., and Nhieu, D. M. Traces inequalities for Carnot-Carathéodory spaces and applications,Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 27, 195–252, (1998).
David, G. and Semmes, S.Fractured Fractals and Broken Dreams, Self-Similar Geometry through Metric and Measure, Oxford University Press, (1997).
De Giorgi, E. Su una teoria generate della misura (r − l)-dimensionale in uno spazio adr dimensioni,Ann. Mat. PuraAppl.(4) 36, 191–213, (1954).
De Giorgi, E. Nuovi teoremi relativi alle misure (r − l)-dimensionali in uno spazio adr dimensioni,Ricerche Mat. 4, 95–113, (1955).
De Giorgi, E. Un progetto di teoria delle correnti, forme differenziali e varietá non orientate in spazi metrici, inVariational Methods, Non Linear Analysys and Differential Equations in Honour of J. P. Cecconi, Genova, Chicco, M. et al., Eds., ECIG, Genova, 67–71, (1993).
De Giorgi, E. Problema di Plateau generale e funzionali geodetici,Atti Sem. Mat. Fis. Univ. Modena 43, 285–292, (1995).
De Giorgi, E. Un progetto di teoria unitaria delle correnti, forme differenziali, varietá ambientate in spazi metrici, funzioni a variazione limitata, manuscript, (1995).
De Giorgi, E., Colombini, F., and Piccinini, L. C. Frontiere orientate di misura minima e questioni collegate,Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) (1972).
Evans, L.C.Partial Differential Equations, Amer. Math. Soc., Providence, (1998).
Federer, H.Geometric Measure Theory, Springer-Verlag, (1969).
Fefferman, C. and Phong, D. H. inSubelliptic Eigenvalue Problems, Beckner et al., Eds., 590–606, (1983).
Folland, G. B. and Stein, E. M.Hardy Spaces on Homogeneous Groups, Princeton University Press, (1982).
Franchi, B., Serapioni, R., and Serra Cassano, F. Meyers-Serrin type theorems and relaxation of variational integrals depending vector fields,Houston J. Math. 22(4), 859–889, (1996).
Franchi, B., Serapioni, R., and Serra Cassano, F. Sur les ensembles des périmètre fini dans le groupe de Heisenberg,C. R. Math. Acad. Sci. Paris, Ser. I, Math.329, 183–188, (1999).
Franchi, B., Serapioni, R., and Serra Cassano, F. Rectifiability and perimeter in the Heisenberg group,Math. Ann. 321, 479–531, (2001).
Franchi, B., Serapioni, R., and Serra Cassano, F. Regular hypersurfaces, intrinsic perimeter and implicit function theorem in Camot groups,Comm. Anal. Geom. 11, 909–944, (2003).
Franchi, B., Serapioni, R., and Serra Cassano, F. On the structure of finite perimeter sets in Step 2 Carnot groups,J. Geom. Anal. 13(3), 421–466, (2003).
Franchi, B., Serapioni, R., and Serra Cassano, F. Regular submanifolds, graphs and area formula in Heisenberg groups, preprint, (2004).
Garofalo, N. and Nhieu, D. M. Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces,Comm. Pure Appl. Math. 49, 1081–1144, (1996).
Gromov, M. Carnot-Carathéodory spaces seen from within, inSubriemannian Geometry, Progress in Mathematics,144, Bellaiche, A. and Risler, J., Eds., Birkhäuser Verlag, Basel, (1996).
Kirchheim, B. Rectifiable metric spaces: Local structure and regularity of the Hausdorff measure,Proc. AMS 121, 113–123, (1994).
Kirchheim, B. and Serra Cassano, F. Rectifiability and parametrization of intrinsic regular surfaces in the Heisenberg group,Ann. Scuola Norm. Sup. Pisa Cl. Sei. (5) III, 871–896, (2004).
Korányi, A. and Reimann, H. M. Foundation for the theory of quasiconformal mappings on the Heisenberg group,Adv. Math. 111, 1–87, (1995).
Lorent, A. Rectifiability of measures with locally uniform cube density,Proc. LMS. (3) 86, 153–249, (2003).
Magnani, V. Differentiability and area formula on stratified Lie groups,Houston J. Math. 27, 297–323, (2001).
Magnani, V. Elements of geometric measure theory on sub-Riemannian groups, tesi di perfezionamento,Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), (2002).
Magnani, V. Characteristic points, rectifiability and perimeter measure on stratified groups, preprint, (2003).
Magnani, V. A blow-up theorem for regular hypersurfaces on nilpotent groups,Manuscripta Math. 110, 55–76, (2003).
Monti, R. Distances, boundaries and surface measures in Carnot-Carathéodory spaces, PhD Thesis, Universitdegli Studi di Trente, (2001).
Monti, R. and Serra Cassano, F. Surface measures in Carnot-Carathéodory spaces,Calc. Var. Partial Diff. Eq. 13, 339–376, (2001).
Nagel, A., Stein, E. M., and Wainger, S. Balls and metrics defined by vector fields I: Basic properties,Acta Math. 155, 103–147, (1985).
Pansu, P. Une inégalité isopérimétrique sur le groupe de Heisenberg,C. R. Math. Acad. Sci. Paris 295(I), 127–130, (1982).
Pansu, P. Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un,Anal. Math. 129, 1–60, (1989).
Pauls, S. D. A notion of rectifiability modelled on Carnot groups,Indiana Univ. Math. J. 53, 49–81, (2004).
Preiss, D. Dimension of metrics and differentiation of measures, inGeneral Topology and its Relations with Analysis, Proc. Fifth Prague Topol. Symp. (1981), Novak, J., Ed., Heldermann-Verlag, Berlin, 565–568, (1982).
Semmes, S. Good metric spaces without good parameterization,Rev. Mat. Iberoamericana 12, 187–275, (1996).
Semmes, S. On the non existence of bilipschitz parametrization and geometric problems about A∞ weights,Rev. Mat. lberoamericana 12, 337–410, (1996).
Stein, E. M.Harmonic Analysis, Princeton University Press, (1993).
Varoupoulos, N. Th., Saloff-Coste, L., and Coulhon, T.Analysis and Geometry on Groups, Cambridge University Press, Cambridge, (1992).