A maximum principle for combinatorial Yamabe flow

Topology

Volumn 44, Issue 4, 2005, Pages 809-825

  Glickenstein, David ^a  

^a University of Arizona   (United States)

Author keywords

Curvature flow; Discrete Riemannian geometry; Laplacians on graphs; Maximum principle; Sphere packing; Yamabe flow

Indexed keywords

EID: 17644370592     PISSN: 00409383     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.top.2005.02.002     Document Type: Article

References (20)

1. H. Berestycki L. Nirenberg S.R.S. Varadhan The principal eigenvalue and maximum principle for second-order elliptic operators in general domains Comm. Pure Appl. Math. 47 1 1994 47-92
2. H.-D. Cao B. Chow Recent developments on the Ricci flow Bull. Amer. Math. Soc. (N.S.) 36 1 1999 59-74
3. B. Chow F. Luo Combinatorial Ricci fl ows on surfaces J. Differential Geom. 63 2003 97-129
4. F.R.K. Chung Spectral graph theory 1997 Published for the Conference Board of the Mathematical Sciences Washington DC
5. F.R.K. Chung R.P. Langlands A combinatorial Laplacian with vertex weights J. Combin. Theory Ser. A 75 2 1996 316-327
6. D. Cooper I. Rivin Combinatorial scalar curvature and rigidity of ball packings Math. Res. Lett. 3 1 1996 51-60
7. T. Coulhon, A. Grigor'yan, F. Zucca, The discrete integral maximum principle and its applications, preprint.
8. J.W. Gaddum The sums of the dihedral and trihedral angles in a tetrahedron Amer. Math. Monthly 59 1952 370-371
9. D. Glickenstein, A combinatorial Yamabe flow in three dimensions, Topology, preprint, 2004, doi:10.1016/j.top.2005.02.001.
10. R.S. Hamilton Three-manifolds with positive Ricci curvature J. Differential Geom. 17 2 1982 255-306
11. R.S. Hamilton, The Ricci flow on surfaces, mathematics and general relativity (Santa Cruz, CA, 1986), Contemporary Mathematics, vol. 71, American Mathematical Society, Providence, RI, 1988, pp. 237-262.
12. R.S. Hamilton, The formation of singularities in the Ricci flow, Surveys in differential geometry, vol. II (Cambridge, MA, 1993), International Press, Cambridge, MA, 1995, pp. 7-136.
13. J.M. Lee T.H. Parker The Yamabe problem Bull. Amer. Math. Soc. (N.S.) 17 1 1987 37-91
14. F. Luo, Combinatorial Yamabe flow on surfaces arXiv:mAth.GT/0306167, 2003.
15. F.H. Lutz, The manifold page, http://www.math.tu-berlin.de/diskregeom/ stellar.
16. F.H. Lutz, Triangulated manifolds with few vertices and vertex-transitive group actions, Berichte aus der Mathematik. [Reports from Mathematics], Verlag Shaker, Aachen, 1999, Dissertation, Technischen Universität Berlin, Berlin, 1999.
17. J. Milnor, The Schläfli differential equality, Collected Papers, vol. 1, Publish or Perish Inc., Houston, TX, 1994, Geometry.
18. P. Padilla The principal eigenvalue and maximum principle for second order elliptic operators on Riemannian manifolds J. Math. Anal. Appl. 205 2 1997 285-312
19. I. Rivin, An extended correction to "Combinatorial Scalar Curvature and Rigidity of Ball Packings," (by D. Cooper and I. Rivin), arXiv:mAth.MG/0302069, 2003.
20. R. Ye Global existence and convergence of Yamabe flow J. Differential Geom. 39 1 1994 35-50