The Uniqueness of Minimal Maps into Cartan-Hadamard Manifolds via the Squared Singular Values

Zhiwei Jia; Minghao Li; Ling Yang

doi:10.1007/s11401-025-0064-6

Chinese Annals of Mathematics, Series B ›› 2026, Vol. 47 ›› Issue (1) :101 -114. DOI: 10.1007/s11401-025-0064-6

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The Uniqueness of Minimal Maps into Cartan-Hadamard Manifolds via the Squared Singular Values

Zhiwei Jia ¹^,^a
, Minghao Li ²^,³^,^b
, Ling Yang ¹^,²^,^c

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Abstract

In this paper, the authors give a uniqueness theorem for the Dirichlet problem of minimal maps into general Riemannian manifolds with non-positive sectional curvature, improving [Lee, YI., Ooi, Y. S. and Tsui, MP., Uniqueness of minimal graph in general codimension, J. Geom. Anal., 29, 2019, 121–133, Theorem 5.2]. The proof of this theorem is based on the convexity of several functions in terms of squared singular values along the geodesic homotopy of two given minimal maps.

Keywords

General codimension / Minimal surface system / Dirichlet problem for minimal maps / Squared singular values / 53A10 / 53C42

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Zhiwei Jia, Minghao Li, Ling Yang. The Uniqueness of Minimal Maps into Cartan-Hadamard Manifolds via the Squared Singular Values. Chinese Annals of Mathematics, Series B, 2026, 47(1): 101-114 DOI:10.1007/s11401-025-0064-6

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References

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[1]	Giusti E, Williams G H. Minimal Surfaces and Functions of Bounded Variation, 1984, Boston, Birkhäuser Vol. 80

[2]	Lawson H B, Osserman R. Non-existence, non-uniqueness and irregularity of solutions to the minimal surface system. Acta Math., 1977, 139: 1-17

[3]	Lee YI, Ooi Y S, Tsui MP. Uniqueness of minimal graph in general codimension. J. Geom. Anal., 2019, 29: 121-133

[4]	Lee YI, Tsui MP. Stability of the minimal surface system and convexity of area functional. Trans. Am. Math. Soc., 2014, 366(7): 3357-3371

[5]	Lee YI, Wang M T. A stability criterion for nonparametric minimal submanifolds. Manuscr. Math., 2003, 112(2): 161-169

[6]	Lee YI, Wang M T. A note on the stability and uniqueness for solutions to the minimal surface system. Math. Res. Lett., 2008, 15(1): 197-206

[7]	Li, M. H., Yang, L. and Zhu, T. Y., A note on the uniqueness of minimal maps into ℝⁿ via singular values, 2023, arXiv: 2311.11075v1.

[8]	Mirsky L. On a convex set of matrices. Arch. Math., 1959, 10: 88-92

[9]	Schoen R. The role of harmonic mappings in rigidity and deformation problems, Complex geometry (Osaka, 1990). Lecture Notes in Pure Appl. Math., 1993, 143: 179-200

[10]	Xu X W, Yang L, Zhang Y S. Dirichlet boundary values on Euclidean balls with infinitely many solutions for the minimal surface system. J. Math. Pures. Appl., 2019, 129: 266-300