minimal submanifolds, Morse index of the volume functional, stability of minimal submanifolds, free boundary minimal submanifolds, spectrum of the Laplacian, Steklov spectrum, Nadirashvili-Friedlander invariants, Robin problem, static manifolds, static manifolds with boundary
D. Cianci, and M. Karpukhin, and V. Medvedev., “On branched minimal immersions of surfaces by first eigenfunctions”, Annals of Global Analysis and Geometry, 56:4 (2019), 667–690
V. Medvedev, “On free boundary minimal submanifolds in geodesic balls in Hn and Sn+”, Mathematische Zeitschrift, 310:1 (2025), 1-35
V. Medvedev, “Degenerating sequences of conformal classes and the conformal Steklov spectrum”, Canadian Journal of Mathematics, 74:4 (2022), 1093-1136
V. Medvedev, “On the Index of the Critical Möbius Band in B4”, The Journal of Geometric Analysis, 3:93 (33), 1-29
V. Medvedev, “Static manifolds with boundary: Their geometry and some uniqueness theorems”, Annales Henri Poincaré, 2026, 1-33
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