Araştırma Makalesi
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VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY

Yıl 2013, Cilt: 6 Sayı: 1, 8 - 40, 30.04.2013

Öz


Kaynakça

  • [1] V. Barone Adesi and F. Serra Cassano and D. Vittone, The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations, Calc. Var and PDE, 30(2007) no.1 , 17-49.
  • [2] Z. Balogh, Size of Characteristic Sets and Functions with Prescribed Gradient., J. fr die Reine und Angewandte Mathematik, 564(2003), 63-83.
  • [3] Bonk, M. and Capogna, L, Mean curvature flow in the Heisenberg group, 2005, preprint.
  • [4] Bryant, R. and Griffiths, P. and Grossman, D., Exterior differential systems and Euler- Lagrange partial differential equations, Chicago Lectures in Mathematics, Chicago, IL, 2003.
  • [5] Capogna, L. and Danielli, D. and Pauls, S. and Tyson, J., An introduction to the Heisen- berg group and the sub-Riemannian isoperimetric problem, Progress in Mathematics, 259, Birkhauser, Basel, 2007.
  • [6] Cheng J.-H. and Hwang J.-F.and Malchiodi, A. and Yang, P., Minimal surfaces in pseudo- hermitian geometry, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4(2005), no. 1, 129-177.
  • [7] Cheng J.-H. and Hwang J.-F. and Yang, P., Existence and uniqueness of p-area minimizers in the Heisenberg group, Math. Ann. 337(2007), no.2, 253-293.
  • [8] Citti, G. and Sarti, A., A cortical based model of perceptual completion in the Roto- Translation space, J. Math. Imaging Vis. 24(2006), 307326.
  • [9] Cole, D., On minimal surfaces in Martinet-type spaces., Ph.D. Thesis, Dartmouth College, 2005.
  • [10] Danielli, D. and Garofalo, N. and Nhieu, D.-M., Sub-Riemannian calculus on hypersurfaces in Carnot groups, Adv. Math 215(2007), no. 1, 292-378.
  • [11] Danielli, D. and Garofalo, N. and Nhieu, D.-M., Minimal surfaces, surfaces of constant mean curvature and isoperimetry in Carnot groups, 2001, preprint.
  • [12] , Danielli, D. and Garofalo, N. and Nhieu, D.-M., A notable family of entire intrinsic min- imal graphs in the Heisenberg group which are not perimeter minimizing, Amer. J. Math. 130(2008), no. 2, 317-339.
  • [13] , Danielli, D. and Garofalo, N. and Nhieu, D.-M. and Pauls, S.,Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group , J. Diff. Geom. 81(2009), no. 2, 251-295.
  • [14] Danielli, D. and Garofalo, N. and Nhieu, D.-M. and Pauls, S., Stable C2 complete embedded noncharacteristic H-minimal surfaces are vertical planes, preprint, arXiv:0903.4296 [math.DG].
  • [15] Derridj, M., Sur un th´eor`eme de traces, Ann. de l’institut Fourier 22(1972), no. 2, 73-83.
  • [16] do Carmo, M. and Peng, C. K.,Stable complete minimal surfaces in R3 are planes, Bull. Amer. Math. Soc. (N.S.) 1(1979), no. 6, 903-906.
  • [17] Fischer-Colbrie, D. and Schoen, R., The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature, Comm. Pure Appl. Math. 33(1980), no. 2, 199- 211.
  • [18] Garofalo, N. and Pauls, S., The Bernstein problem in the Heisenberg group., preprint, arXiv:math/0209065 [math.DG].
  • [19] Hirsch, M.W., Differential Topology, Springer-Verlag, 1997.
  • [20] Hladky, R. and Pauls, S., Constant Mean Curvature Surfaces in sub-Riemannian Geometry, J. Diff. Geom. 79(2008), no. 1, 111-139.
  • [21] Hladky, R., Connections and curvature in sub-Riemannian geometry, Houston J. Math. 38(2012), no. 4, 1107-1134.
  • [22] Hoffman, W., The visual cortex is a contact bundle, Appl. Math. Comput. 32(1989), no. 2-3, 137-167.
  • [23] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, John Wiley & Sons, Inc., 1963.
  • [24] Leonardi, G. P. and Rigot, S., Isoperimetric sets on Carnot groups, Houston J. Math. 29(2003), no. 3, 609-637.
  • [25] Magnani, V., Characteristic points, rectifiability and perimeter measure on stratified groups, J. Eur. Math. Soc. 8(2006), no. 4, 585-609.
  • [26] Magnani, V., Differentiability and Area Fomula on Stratified Lie groups, preprint.
  • [27] Montefalcone,F., Hypersurfaces and variational formulas in sub-Riemannian Carnot groups, J. Math. Pures Appl. 87(2007), 453-494.
  • [28] Monti, R. and Rickly, M., Convex isoperimetric sets in the Heisenberg group, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 8 (2009), no. 2, 391-415.
  • [29] Pansu, P., M´etriques de Carnot-Carath´eodory et quasiisom´etries des espaces sym´etriques de rang un, Annals of Mathematics (2) 129(1989), no. 1, 1-60.
  • [30] Pauls, S., Minimal surfaces in the Heisenberg group., Geom. Ded. 104(2004), 201-231.
  • [31] Petitot, J., The neurogeometry of pinwheels as a sub-Riemannian contact structure, J. Phys- iology 97(2003), 265–309.
  • [32] J. Petitot and Y. Tondut, Vers une neuro-geometrie. Fibrations corticales, structures de contact et contours subjectifs modaux., Math., Info. et Sc. Hum., EHESS, Paris 145(1998), 5–101.
  • [33] Ritor´e, M. and Rosales, C., Area-stationary surfaces in the Heisenberg group H1, Mat. Con- temp. 35 (2008), 185-203.
  • [34] Ritor´e, M. and Rosales, C., Rotationally invariant hypersurfaces with constant mean curva- ture in the Heisenberg group Hn, J. Geom. Anal. 16 (2006), no. 4, 703720.
  • [35] Selby, C., Geometry of hypersurfaces in Carnot groups of step two., Ph.D. Thesis, Purdue University, 2006.
  • [36] Shcherbakova, N., Minimal surfaces in contact sub-Riemannian manifolds, preprint, arXiv:math/0604494 [math.DG].
  • [37] N. Tanaka, A differential geometric study on strongly pseudoconvex manifolds., Kinokuniya Book-Store Co., Ltd., 1975.
  • [38] S.M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Diff. Geom., 13(1978), 25-41.
Yıl 2013, Cilt: 6 Sayı: 1, 8 - 40, 30.04.2013

Öz

Kaynakça

  • [1] V. Barone Adesi and F. Serra Cassano and D. Vittone, The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations, Calc. Var and PDE, 30(2007) no.1 , 17-49.
  • [2] Z. Balogh, Size of Characteristic Sets and Functions with Prescribed Gradient., J. fr die Reine und Angewandte Mathematik, 564(2003), 63-83.
  • [3] Bonk, M. and Capogna, L, Mean curvature flow in the Heisenberg group, 2005, preprint.
  • [4] Bryant, R. and Griffiths, P. and Grossman, D., Exterior differential systems and Euler- Lagrange partial differential equations, Chicago Lectures in Mathematics, Chicago, IL, 2003.
  • [5] Capogna, L. and Danielli, D. and Pauls, S. and Tyson, J., An introduction to the Heisen- berg group and the sub-Riemannian isoperimetric problem, Progress in Mathematics, 259, Birkhauser, Basel, 2007.
  • [6] Cheng J.-H. and Hwang J.-F.and Malchiodi, A. and Yang, P., Minimal surfaces in pseudo- hermitian geometry, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4(2005), no. 1, 129-177.
  • [7] Cheng J.-H. and Hwang J.-F. and Yang, P., Existence and uniqueness of p-area minimizers in the Heisenberg group, Math. Ann. 337(2007), no.2, 253-293.
  • [8] Citti, G. and Sarti, A., A cortical based model of perceptual completion in the Roto- Translation space, J. Math. Imaging Vis. 24(2006), 307326.
  • [9] Cole, D., On minimal surfaces in Martinet-type spaces., Ph.D. Thesis, Dartmouth College, 2005.
  • [10] Danielli, D. and Garofalo, N. and Nhieu, D.-M., Sub-Riemannian calculus on hypersurfaces in Carnot groups, Adv. Math 215(2007), no. 1, 292-378.
  • [11] Danielli, D. and Garofalo, N. and Nhieu, D.-M., Minimal surfaces, surfaces of constant mean curvature and isoperimetry in Carnot groups, 2001, preprint.
  • [12] , Danielli, D. and Garofalo, N. and Nhieu, D.-M., A notable family of entire intrinsic min- imal graphs in the Heisenberg group which are not perimeter minimizing, Amer. J. Math. 130(2008), no. 2, 317-339.
  • [13] , Danielli, D. and Garofalo, N. and Nhieu, D.-M. and Pauls, S.,Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group , J. Diff. Geom. 81(2009), no. 2, 251-295.
  • [14] Danielli, D. and Garofalo, N. and Nhieu, D.-M. and Pauls, S., Stable C2 complete embedded noncharacteristic H-minimal surfaces are vertical planes, preprint, arXiv:0903.4296 [math.DG].
  • [15] Derridj, M., Sur un th´eor`eme de traces, Ann. de l’institut Fourier 22(1972), no. 2, 73-83.
  • [16] do Carmo, M. and Peng, C. K.,Stable complete minimal surfaces in R3 are planes, Bull. Amer. Math. Soc. (N.S.) 1(1979), no. 6, 903-906.
  • [17] Fischer-Colbrie, D. and Schoen, R., The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature, Comm. Pure Appl. Math. 33(1980), no. 2, 199- 211.
  • [18] Garofalo, N. and Pauls, S., The Bernstein problem in the Heisenberg group., preprint, arXiv:math/0209065 [math.DG].
  • [19] Hirsch, M.W., Differential Topology, Springer-Verlag, 1997.
  • [20] Hladky, R. and Pauls, S., Constant Mean Curvature Surfaces in sub-Riemannian Geometry, J. Diff. Geom. 79(2008), no. 1, 111-139.
  • [21] Hladky, R., Connections and curvature in sub-Riemannian geometry, Houston J. Math. 38(2012), no. 4, 1107-1134.
  • [22] Hoffman, W., The visual cortex is a contact bundle, Appl. Math. Comput. 32(1989), no. 2-3, 137-167.
  • [23] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, John Wiley & Sons, Inc., 1963.
  • [24] Leonardi, G. P. and Rigot, S., Isoperimetric sets on Carnot groups, Houston J. Math. 29(2003), no. 3, 609-637.
  • [25] Magnani, V., Characteristic points, rectifiability and perimeter measure on stratified groups, J. Eur. Math. Soc. 8(2006), no. 4, 585-609.
  • [26] Magnani, V., Differentiability and Area Fomula on Stratified Lie groups, preprint.
  • [27] Montefalcone,F., Hypersurfaces and variational formulas in sub-Riemannian Carnot groups, J. Math. Pures Appl. 87(2007), 453-494.
  • [28] Monti, R. and Rickly, M., Convex isoperimetric sets in the Heisenberg group, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 8 (2009), no. 2, 391-415.
  • [29] Pansu, P., M´etriques de Carnot-Carath´eodory et quasiisom´etries des espaces sym´etriques de rang un, Annals of Mathematics (2) 129(1989), no. 1, 1-60.
  • [30] Pauls, S., Minimal surfaces in the Heisenberg group., Geom. Ded. 104(2004), 201-231.
  • [31] Petitot, J., The neurogeometry of pinwheels as a sub-Riemannian contact structure, J. Phys- iology 97(2003), 265–309.
  • [32] J. Petitot and Y. Tondut, Vers une neuro-geometrie. Fibrations corticales, structures de contact et contours subjectifs modaux., Math., Info. et Sc. Hum., EHESS, Paris 145(1998), 5–101.
  • [33] Ritor´e, M. and Rosales, C., Area-stationary surfaces in the Heisenberg group H1, Mat. Con- temp. 35 (2008), 185-203.
  • [34] Ritor´e, M. and Rosales, C., Rotationally invariant hypersurfaces with constant mean curva- ture in the Heisenberg group Hn, J. Geom. Anal. 16 (2006), no. 4, 703720.
  • [35] Selby, C., Geometry of hypersurfaces in Carnot groups of step two., Ph.D. Thesis, Purdue University, 2006.
  • [36] Shcherbakova, N., Minimal surfaces in contact sub-Riemannian manifolds, preprint, arXiv:math/0604494 [math.DG].
  • [37] N. Tanaka, A differential geometric study on strongly pseudoconvex manifolds., Kinokuniya Book-Store Co., Ltd., 1975.
  • [38] S.M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Diff. Geom., 13(1978), 25-41.
Toplam 38 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Robert K. Hladky Bu kişi benim

Scott D. Pauls Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 6 Sayı: 1

Kaynak Göster

APA Hladky, R. K., & Pauls, S. D. (2013). VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY. International Electronic Journal of Geometry, 6(1), 8-40.
AMA Hladky RK, Pauls SD. VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY. Int. Electron. J. Geom. Nisan 2013;6(1):8-40.
Chicago Hladky, Robert K., ve Scott D. Pauls. “VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY”. International Electronic Journal of Geometry 6, sy. 1 (Nisan 2013): 8-40.
EndNote Hladky RK, Pauls SD (01 Nisan 2013) VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY. International Electronic Journal of Geometry 6 1 8–40.
IEEE R. K. Hladky ve S. D. Pauls, “VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY”, Int. Electron. J. Geom., c. 6, sy. 1, ss. 8–40, 2013.
ISNAD Hladky, Robert K. - Pauls, Scott D. “VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY”. International Electronic Journal of Geometry 6/1 (Nisan 2013), 8-40.
JAMA Hladky RK, Pauls SD. VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY. Int. Electron. J. Geom. 2013;6:8–40.
MLA Hladky, Robert K. ve Scott D. Pauls. “VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY”. International Electronic Journal of Geometry, c. 6, sy. 1, 2013, ss. 8-40.
Vancouver Hladky RK, Pauls SD. VARIATION OF PERIMETER MEASURE IN SUB-RIEMANNIAN GEOMETRY. Int. Electron. J. Geom. 2013;6(1):8-40.