Geodesic
Minimal surfaces and the new main inequality
Vladimir Marković1 ; Nathaniel Sagman2
1 University of Oxford, All Souls College
2 University of Luxembourg
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 99–117.

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We establish the new main inequality as a minimizing criterion for minimal maps into products of $\mathbb{R}$-trees, and the infinitesimal new main inequality as a stability criterion for minimal maps to $\mathbb{R}^n$. Along the way, we develop a new perspective on destabilizing minimal surfaces in $\mathbb{R}^n$, and as a consequence we reprove the instability of some classical minimal surfaces; for example, the Enneper surface.  
DOI : 10.54330/afm.143716
Keywords: Minimal surfaces, quasiconformal maps, harmonic maps, real trees

Vladimir Marković 1 ; Nathaniel Sagman 2

1 University of Oxford, All Souls College
2 University of Luxembourg 
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Vladimir Marković; Nathaniel Sagman. Minimal surfaces and the new main inequality. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 99–117. doi : 10.54330/afm.143716. http://geodesic.mathdoc.fr/articles/10.54330/afm.143716/

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