Geodesic
Isotropic Hypersurfaces and Minimal Extensions of Lipschitz Functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 28-36.

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The existence and uniqueness theorem for isotropic hypersurfaces with prescribed boundary in Lorentzian warped products is proved. The proof is based on minimal Lipschitz extensions of functions.
Mots-clés : Lorentzian space
Keywords: isotropic surface, Lipschitz function, minimal extension of a Lipschitz function. 
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A. A. Klyachin; V. M. Miklyukov. Isotropic Hypersurfaces and Minimal Extensions of Lipschitz Functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 28-36. http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a2/

[1] Bim Dzh., Erlikh P., Globalnaya lorentseva geometriya, Mir, M., 1990 | MR

[2] Klyachin A. A., Miklyukov V. M., “Sledy funktsii s prostranstvennopodobnymi grafikami i zadacha o prodolzhenii pri ogranicheniyakh na gradient”, Matem. sb., 183:7 (1992), 49–64 | MR

[3] Grigoryeva E., Klyachin A., Miklyukov V., “Problem of functional extension and space-like surfaces in Minkowski space”, Z. Anal. Anwendungen, 21 (2002), 719–752 | DOI | MR | Zbl

[4] Bartnik R., Simon L., “Spacelike hypersurfaces with prescribed boundary values and mean curvature”, Commun. Math. Phys., 87 (1982/83), 131–152 | DOI | MR | Zbl

[5] Klyachin A. A., Miklyukov V. M., “Suschestvovanie reshenii s osobennostyami uravneniya maksimalnykh poverkhnostei v prostranstve Minkovskogo”, Matem. sb., 184:9 (1993), 103–124 | MR | Zbl

[6] Aronsson G., “Extension of functions satisfying Lipschitz conditions”, Ark. Mat., 6:28 (1967), 551–561 | DOI | MR | Zbl

[7] Jensen R., “Uniqueness of Lipschitz extension: minimizing the sup norm of the gradient”, Arch. Rational Mech. Anal., 123 (1993), 51–74 | DOI | MR | Zbl

[8] Crandall M. G., Evans L. C., Gariepy R. F., “Optimal Lipschitz extensions and the infinity Laplacian”, Calc. Var. Partial Differential Equations, 13:2 (2001), 123–139 | DOI | MR | Zbl

[9] Juutinen P., “Absolutely minimizing Lipschitz extensions on a metric space”, Ann. Acad. Sci. Fenn., Ser. AI Math., 27 (2002), 57–67 | MR | Zbl

[10] Federer G., Geometricheskaya teoriya mery, Nauka, M., 1987 | MR | Zbl

[11] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, Nauka, M., 1979 | MR

[12] Bishop R. L., Krittenden R. Dzh., Geometriya mnogoobrazii, Mir, M., 1967 | MR | Zbl

[13] McShane E. J., “Extension of range of functions”, Bull. Amer. Math. Soc., 40 (1934), 837–842 | DOI | MR | Zbl

[14] Whitney H., “Analytic extensions of differentiable functions defined in closed sets”, Trans. Amer. Math. Soc., 36 (1934), 63–89 | DOI | MR | Zbl

[15] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, t. 2, Nauka, M., 1981 | MR