arXiv subjects

Nicolau Sarquis Aiex

Publications and source records attributed to Nicolau Sarquis Aiex.

3 recordsLinked to original sources

arXiv2018

Index Estimate of Self-Shrinkers in $\mathbb{R}^3$ with Asymptotically Conical Ends

We construct Gaussian Harmonic forms of finite Gaussian weighted $L^2$-norm on non-compact surfaces that detect each asymptotically conical end. As an application we prove an extension of the index estimates of self-shrinkers in $[11]$ under the existence of such ends. We show that the Morse index of a self-shrinker is greater or equal to $\frac{2g+r-1}{3}$, where $r$ is the number of asymptotically conical ends.

math.DG↗

arXiv2016

Non-compactness of the space of minimal hypersurfaces

We show that the space of min-max minimal hypersurfaces is non-compact when the manifold has an analytic metric of positive Ricci curvature and dimension $3\leq n+1\leq 7$. Furthermore, we show that bumpy metrics with positive Ricci curvature admit minimal hypersurfaces with unbounded index+area. When combined with the recent work fo F.C. Marques and A. Neves, we then deduce some new properties regarding the infinitely many minimal hypersurfaces they found.

math.DG↗

arXiv2016

The Width of Ellipsoids

We compute the $k$-width of a round $2$-sphere for $k=1,\ldots,8$ and we use this result to show that unstable embedded closed geodesics can arise with multiplicity as a min-max critical varifold.

math.DG↗