13 citations · 14 across the 8 of their papers we have counts for
12 papers
Insights from Autoresearch for Solar Panel Segmentation
Justinas Lekavicius, Kursat Komurcu, Valentas Gruzauskas +1
This paper investigates AutoResearch, a protocol in which a coding language model edits a training program under a one-hour GPU budget and retains a change only if validation IoU i…
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…
Second order estimates on transition layers for the Allen-Cahn equation with homogeneous Neumann boundary conditions: Part I - Boundary-orthogonal transition layers
Akashdeep Dey, Wenkui Du, Davide Parise +1
We study stable solutions of the Allen-Cahn equation with homogeneous Neumann boundary condition on Riemannian manifolds with boundary in the regime where the transition layers mee…
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…
Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents
Paul Minter, Davide Parise, Anna Skorobogatova +1
We prove that the singular set of an -dimensional integral current in , semicalibrated by a -form is countably -rectifiable.…
Quantitative stability of Sobolev inequalities on compact Riemannian manifolds
Francesco Nobili, Davide Parise
We study quantitative stability results for different classes of Sobolev inequalities on general compact Riemannian manifolds. We prove that, up to constants depending on the manif…
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…