On functional separately convex hulls

Discrete and Computational Geometry

Volumn 19, Issue 1, 1998, Pages 105-130

  Matousek J ^a   Plechac P ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039572462     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009331     Document Type: Article

References (17)

1. R. Aumann and S. Hart, Bi-convexity and bi-martingales, Israel. J. Math. 54, 2 (1986), 159-180.
2. J. M. Ball, Sets of gradients with no rank-one connections, J. Math. Pures Appl. 69 (1990), 241-259.
3. K. Bhattacharya, N. B. Firoozye, R. D. James, and R. V. Kohn, Restrictions on microstructures, Proc. Roy. Soc. Edinburgh, 124A (1994), 843-878.
4. J. M. Ball and R. James, Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal. 100 (1987), 15-52.
5. V. Chvátal, Linear Programming, Freeman, New York, 1983.
6. C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966.
7. T. Ottmann, E. Soisalon-Soininen, and D. Wood, On the definition and computation of rectilinear convex hulls. Inform. Sci. 33 (1985), 157-171.
8. F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.
9. G. J. E. Rawlins and D. Wood, Optimal computation of finitely oriented convex hulls, Inform. Comput. 72 (1987), 150-166.
10. G. J. E. Rawlins and D. Wood, Computational geometry with restricted orientations, Proc. 13th IFIP Conf. System Modelling and Optimization, Lecture Notes in Control and Information Science, vol. 113, Springer-Verlag, Berlin, 1988, pp. 375-384.
11. G. J. E. Rawlins and D. Wood, Ortho-convexity and its generalizations, in (G. T. Toussaint, ed.), Computational Morphology, North-Holland, Amsterdam, 1988, pp. 137-152.
12. V. Šverák, Rank-one convexity does not imply quasiconvexity. Proc. Roy. Soc. Edinburgh, 120A (1992), 185-189.
13. V. Šverák, On Tartar's conjectures, Ann. Inst. H. Poincaré, 10 (1993), 405-412.
14. V. Šverák, On the problem of two wells, in (D. Kinderlehrer, R. James, M. Luskin, and J. L. Ericksen, eds.), Microstructure and Phase Transition, The IMA Volumes in Mathematics and its Applications, vol. 54, Springer-Verlag, New York, 1993.
15. L. Tartar, On separately convex functions, in (D. Kinderlehrer, R. James, M. Luskin, and J. L. Ericksen, eds.), Microstructure and Phase Transition, The IMA Volumes in Mathematics and its Applications, vol. 54, Springer-Verlag, New York, 1993.
16. K. Zhang, On connected subset of M2×2 without rank-one connections, Technical report, School of Mathematics, Macquarie University, NSW 2109, Australia, 1994.
17. K. Zhang, Personal communication.