Voir la notice de l'article provenant de la source Math-Net.Ru
@article{INTO_2024_236_a2, author = {S. E. Stepanov and I. I. Tsyganok}, title = {A contribution of the generalized {Bochner} technique to the geometry of complete minimal submanifolds}, journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory}, pages = {22--30}, publisher = {mathdoc}, volume = {236}, year = {2024}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/INTO_2024_236_a2/} }
TY - JOUR AU - S. E. Stepanov AU - I. I. Tsyganok TI - A contribution of the generalized Bochner technique to the geometry of complete minimal submanifolds JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2024 SP - 22 EP - 30 VL - 236 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2024_236_a2/ LA - ru ID - INTO_2024_236_a2 ER -
%0 Journal Article %A S. E. Stepanov %A I. I. Tsyganok %T A contribution of the generalized Bochner technique to the geometry of complete minimal submanifolds %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2024 %P 22-30 %V 236 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2024_236_a2/ %G ru %F INTO_2024_236_a2
S. E. Stepanov; I. I. Tsyganok. A contribution of the generalized Bochner technique to the geometry of complete minimal submanifolds. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 2, Tome 236 (2024), pp. 22-30. http://geodesic.mathdoc.fr/item/INTO_2024_236_a2/
[1] Grigoryan A. A., “Stokhasticheski polnye mnogoobraziya i summiruemye garmonicheskie funktsii”, Izv. AN SSSR. Ser. mat., 52:5 (1988), 1102–1108
[2] Stepanov S. E., Tsyganok I. I., “Potochechnoe ortogonalnoe rasscheplenie prostranstva TT-tenzorov”, Differ. geom. mnogoobr. figur., 54:2 (2023), 45–53
[3] Besse A., Einstein Manifolds, Springer, Berlin, 1987
[4] Carlotto A., “The general relativistic constraint equations”, Living Rev. Relativ., 24 (2021), 2
[5] do Carmo M. P., Chern S. S., Kobayashi S., “Minimal submanifolds of a sphere with second fundamental form of constant length”, Functional Analysis and Related Fields, ed. Browder F. E., Springer-Verlag, Berlin–Heidelberg–New York, 1970, 59–75
[6] Catino G., Mastrolia P., Roncoroni A., “Two rigidity results for stable minimal hypersurfaces”, Geom. Funct. Anal., 34 (2024), 1–18
[7] Chen B.-Y., “Riemannian submanifolds”, Handbook of Differential Geometry. Vol. 1, eds. Dillen F. J. E., Verstraelen L. C. A., North Holland, Amsterdam, 2000, 187–418
[8] Cheng S. Y., Yau S.-T., “Differential equations on Riemannian manifolds and their geometric applications”, Commun. Pure Appl. Math., 28:3 (1975), 333–354
[9] Eisenhart L. P., “Symmetric tensor of the second order whose first covariant derivatives are zero”, Trans. Am. Math. Soc., 25:2 (1923), 297–306
[10] Fu H.-P., Xu G.-B., Tao Y.-Q., “Some remarks on Riemannian manifolds with parallel Cotton tensor”, Kodai Math. J., 42:1 (2019), 64–74
[11] Grigor'yan A., “Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds”, Bull. Am. Math. Soc., 36:2 (1999), 135–249
[12] Li P., Wang J., “Stable minimal hypersurfaces in a non-negatively curved manifold”, J. Reine Angew. Math., 566 (2004), 215–230
[13] Mikeš J., Stepanov S., “What is the Bochner technique and where is it applied”, Lobachevskii J. Math., 43:4 (2022), 709–719
[14] Petersen P., Riemannian Geometry, Springer, Cham, 2016
[15] Pierzchalski A., “Gradients: The ellipticity and the elliptic boundary conditions — a jigsaw puzzle”, Folia Math., 19:1 (2017), 65–83
[16] Pigola S., Rigoli M., Setti A. G., Vanishing and Finiteness Results in Geometric Analysis. A Generalization of the Bochner Technique, Birkhäuser, Basel–Boston–Berlin, 2008
[17] Shandra I. G., Stepanov S. E., Mikeš J., “On higher-order Codazzi tensors on complete Riemannian manifolds”, Ann. Glob. Anal. Geom., 56 (2019), 429–442
[18] Simons J., “Minimal varieties in Riemannian manifolds”, Ann. Math., 88:1 (1968), 62–105
[19] Yau S.-T., “Some function-theoretic properties of complete Riemannian manifold and their applications to geometry”, Indiana Univ. Math. J., 25:7 (1976), 659–670
[20] Yau S.-T., “Erratum: Some function-theoretic properties of complete Riemannian manifold and their applications to geometry”, Indiana Univ. Math. J., 31:4 (1982), 607–607