13 citations · 14 across the 8 of their papers we have counts for
8 papers · 1 filter
Boundary behaviour of stable Allen-Cahn limit-interfaces in Riemannian manifolds
Martin Man-chun Li, Davide Parise, Lorenzo Sarnataro
This is the second paper in our series of works to develop the min-max theory for free boundary minimal hypersurfaces in Riemannian manifolds with boundary via the Allen-Cahn equat…
White's cone over the Möbius band is area-minimising
Marco A. M. Guaraco, Davide Parise
We prove that the cone in over a suitable minimal Möbius band is locally mass-minimising with coefficients in . This proves…
Uniqueness of free boundary minimal annuli
Davide Parise, Jonathan J. Zhu
We prove that every smooth properly embedded free-boundary minimal annulus in the unit ball is congruent to the critical catenoid. We also classify positive solutions of $(Δ_{\math…
Generic regularity of isoperimetric regions in dimension eight
Kobe Marshall-Stevens, Gongping Niu, Davide Parise
We establish generic regularity results for isoperimetric regions in closed Riemannian manifolds of dimension eight. In particular, we show that every isoperimetric region has a sm…
Symmetric log-epiperimetric inequality for harmonic maps with analytic target and applications
Riccardo Caniato, Davide Parise
We establish a direct symmetric (log)-epiperimetric inequality for harmonic maps with analytic target and we leverage on this result to achieve a new proof of Simon's celebrated un…
Almost minimizing YangMills fields: log-epiperimetric inequality, non-concentration, and uniqueness of tangents
Riccardo Caniato, Davide Parise
We establish a direct log-epiperimetric inequality for YangMills fields in arbitrary dimension and we leverage on it to prove uniqueness of tangent cones with isolated singulari…
Boundary behavior of limit-interfaces for the Allen-Cahn equation on Riemannian manifolds with Neumann boundary condition
Martin Li, Davide Parise, Lorenzo Sarnataro
We study the boundary behavior of any limit-interface arising from a sequence of general critical points of the Allen-Cahn energy functionals on a smooth bounded domain. Given any…
Warped Tori with Almost Non-Negative Scalar Curvature
Brian Allen, Lisandra Hernandez-Vazquez, Davide Parise +2
For sequences of warped product metrics on a -torus satisfying the scalar curvature bound , uniform upper volume and diameter bounds, and a uniform lower…