3 problems

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Chanillo–Malchiodi non-degeneracy conjecture for higher-degree H-bubbles
Chanillo–Malchiodi non-degeneracy conjecture. The higher-degree $H$ -bubble $\pi(z^m)$ with $|m|\geq 2$ is non-degenerate for the energy functional.
Conjecturesolvedgeometric-analysis h-systems non-degeneracyarXiv posted 2 days ago
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The non-degeneracy conjecture for solutions of the non-critical $SU(3)$ Toda system
Non-degeneracy conjecture. Except for finitely many $\tau$ modulo the $SL(2,\mathbb{Z})$ action, every solution of the Toda system is non-degenerate. If true, this would support th…
Conjectureopenelliptic-pdes non-degeneracy toda-systemsarXiv posted 2 days ago
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All nonpositive-curvature Riemannian Schwarzschild–anti de Sitter metrics are non-degenerate
Non-degeneracy conjecture. The known ranges of mass parameters are not sharp, and the proposed arguments can establish non-degeneracy for all values of $\mu$ when $K\leq 0$ .
Conjectureopengeneral-relativity non-degeneracy riemannian-geometryarXiv posted 2 days ago

Chanillo–Malchiodi non-degeneracy conjecture for higher-degree H-bubbles