For any smooth Riemannian metric on an (n+ 1)(n+ 1)-dimensional compact manifold with
boundary (M, ∂ M)(M,∂ M) where 3 ≤ (n+ 1) ≤ 7 3≤(n+ 1)≤ 7, we establish general …

We prove the multiplicity one theorem for min-max free boundary minimal hypersurfaces in
compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To …

In this paper, we prove that in any compact Riemannian manifold with smooth boundary, of
dimension at least $3 $ and at most $7 $, there exist infinitely many almost properly …

For a closed Riemannian manifold M n+ 1 with a compact Lie group G acting as isometries,
the equivariant min–max theory gives the existence and the potential abundance of minimal …

For a compact Riemannian manifold $ M^{n+ 1} $ acted isometrically on by a compact Lie
group $ G $ with cohomogeneity ${\rm Cohom}(G)\geq 2$, we show the Weyl asymptotic law …

For almost all Riemannian metrics (in the $ C^\infty $ Baire sense) on a compact manifold
with boundary $(M^{n+ 1},\break\partial M) $, $3\leq (n+ 1)\leq 7$, we prove that, for any …