Study of tree automorphisms via arc-stabilizers.
problem Understanding automorphisms of -trees.
method Analyzing actions over arc-stabilizers.
result Point-stabilizers are finitely generated.
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Proves results on K-stability using arcs and Mabuchi functional.
problem K-stability in Fano manifolds and uniform K-polystability.
method Arcs and numerical criterion for stability of pairs.
result Characterizes coercivity of Mabuchi functional in terms of K-polystability.
Let be a countable group that splits as a free product of groups of the form , where is a finitely generated free group. We identify the closure of the outer space for the axes topology with the space of projective minimal, \emph{very small} …