Geodesic
Maximal tubular surfaces of arbitrary codimension in the Minkowski space
Izvestiya. Mathematics , Tome 43 (1994) no. 1, pp. 105-118.

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A surface, given by a $C^2$-immersion $u\colon M\to R_1^{n+1}$, is said to be tubular if the cross-sections $u(M)\cap\Pi$ are compact for all hyperplanes $\Pi$ that are orthogonal to the time axis. Space-like surfaces with zero mean curvature vector are maximal. The extrinsic properties of maximal tubular surfaces are studied in this paper. In particular, it is proved that if such a surface, of dimension $p\geqslant 3$, has a singularity, then it has finite spread along the time axis. 
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V. A. Klyachin. Maximal tubular surfaces of arbitrary codimension in the Minkowski space. Izvestiya. Mathematics , Tome 43 (1994) no. 1, pp. 105-118. http://geodesic.mathdoc.fr/item/IM2_1994_43_1_a5/

[1] Bim Dzh., Erlikh P., Globalnaya lorentseva geometriya, Mir, M., 1985, 400 pp. | MR

[2] Ecker K., “Area maximizing hypersurfaces in Minkowski space having an isolated singularity”, Manuscr. Math., 56 (1986), 375–397 | DOI | MR | Zbl

[3] Bartnik R., Simon L., “Spacelike hypersurfaces with prescribed boundary values and mean curvature”, Comm. Math. Phys., 87:1 (1982), 131–152 | DOI | MR | Zbl

[4] Cheng S., Yau S.-T., “Maximal spacelike hypersurfaces in the Lorentz–Minkowski spaces”, Ann. of Math., 104:2 (1976), 407–419 | DOI | MR | Zbl

[5] Vedenyapin A. D., Miklyukov V. M., “Vneshnie razmery trubchatykh minimalnykh giperpoverkhnostei”, Matem. sb., 131 (1986), 240–250 | MR | Zbl

[6] Klyachin V. A., Miklyukov V. M., “Maksimalnye giperpoverkhnosti trubchatogo tipa v prostranstve Minkovskogo”, Izv. AN SSSR. Ser. matem., 55:1 (1991), 206–217 | MR

[7] Miklyukov V. M., “O nekotorykh svoistvakh trubchatykh v tselom minimalnykh poverkhnostei v $\mathbf{R}^n$”, DAN SSSR, 247:3 (1979), 549–552 | MR | Zbl

[8] Miklyukov V. M., Tkachev V. G., “Nekotorye svoistva trubchatykh minimalnykh poverkhnostei proizvolnoi korazmernosti”, Matem. sb., 180:9 (1989), 1278–1295 | MR | Zbl

[9] Miklyukov V. M., “O konformnom tipe kontsov maksimalnykh prostranstvenno-podobnykh poverkhnostei s osobennostyami”, Aktualnye voprosy kompleksnogo analiza, Tez. dokl. shkoly-seminara, Tashkent, 1989 | Zbl

[10] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, v. 2, Nauka, M., 1981, 414 pp.

[11] Goldshtein V. M., Reshetnyak Yu. G., Vvedenie v teoriyu-funktsii s obobschennymi proizvodnymi i kvazikonformnye otobrazheniya, Nauka, M., 1983, 284 pp. | MR

[12] Burago Yu. D., Zalgaller V. L., Geometricheskie neravenstva, Nauka, L., 1980, 288 pp. | MR | Zbl

[13] Suvorov G. D., Obobschennyi “printsip dliny i ploschadi” v teorii otobrazhenii, Nauk. dumka, Kiev, 1985, 280 pp. | MR

[14] Vladimirov B. C., Uravneniya matematicheskoi fiziki, 5-e izd., dop., Nauka, M., 1988, 512 pp. | MR