ﻻ يوجد ملخص باللغة العربية
Given any admissible $k$-dimensional family of immersions of a given closed oriented surface into an arbitrary closed Riemannian manifold, we prove that the corresponding min-max width for the area is achieved by a smooth (possibly branched) immersed minimal surface with multiplicity one and Morse index bounded by $k$.
We adapt the viscosity method introduced by Rivi`ere to the free boundary case. Namely, given a compact oriented surface $Sigma$, possibly with boundary, a closed ambient Riemannian manifold $(mathcal{M}^m,g)$ and a closed embedded submanifold $mathc
For any smooth Riemannian metric on an $(n+1)$-dimensional compact manifold with boundary $(M,partial M)$ where $3leq (n+1)leq 7$, we establish general upper bounds for the Morse index of free boundary minimal hypersurfaces produced by min-max theory
We establish a new estimate for the Ginzburg-Landau energies $E_{epsilon}(u)=int_Mfrac{1}{2}|du|^2+frac{1}{4epsilon^2}(1-|u|^2)^2$ of complex-valued maps $u$ on a compact, oriented manifold $M$ with $b_1(M) eq 0$, obtained by decomposing the harmonic
We use min-max techniques to produce nontrivial solutions $u_{epsilon}:Mto mathbb{R}^2$ of the Ginzburg-Landau equation $Delta u_{epsilon}+frac{1}{epsilon^2}(1-|u_{epsilon}|^2)u_{epsilon}=0$ on a given compact Riemannian manifold, whose energy grows
In this short paper, we will give a simple and transcendental proof for Moks theorem of the generalized Frankel conjecture. This work is based on the maximum principle in cite{BS2} proposed by Brendle and Schoen.