N. S. Aiex

activity

20162024

collaborators

4 papers

math.DG2024

A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by $C^{1, α}$ Multiple Valued Functions

Nicolau S. Aiex

We provide a counter-example to Hutchinson's original proof of $C^{1, α}$ representation of curvature $m$ -varifolds with $L^{q}$ -integrable second fundamental form and $q > m$ in [6]. W…

math.DG2019

Index Estimates for Surfaces with Constant Mean Curvature in $3$ -dimensional Manifolds

Nicolau S. Aiex, Han Hong

We prove index estimates for closed and free boundary CMC surfaces in certain $3$ -dimensional submanifolds of some Euclidean space. When the mean curvature is large enough we are a…

math.DG2018

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

Nicolau Sarquis Aiex

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 exten…

math.DG2016

The Width of Ellipsoids

Nicolau Sarquis Aiex

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

A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by C1,α Multiple Valued Functions

Index Estimates for Surfaces with Constant Mean Curvature in 3-dimensional Manifolds

Index Estimate of Self-Shrinkers in R3 with Asymptotically Conical Ends

The Width of Ellipsoids

A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by $C^{1, α}$ Multiple Valued Functions

Index Estimates for Surfaces with Constant Mean Curvature in $3$ -dimensional Manifolds

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