Nicolau Sarquis Aiex

nsarquis 'at' math.ntnu.edu.tw

Postdoctoral fellow at NTNU.

PhD in Pure Mathematics by Imperial College London under supervision of professor André Neves. Interested in geometric analysis and differential geometry.

CV (Oct 2025)

Brief Research Summary

My research area lies in the intersection of Geometric Measure Theory, Analysis and Differential Geometry.

More precisely, the problems I am interested are in the GMT set up and I use geometric analysis tools such as Almgren-Pitts min-max and analysis of singularities to study variational objects such as minimal submanifolds, surfaces of constant mean curvature and self-shrinking surfaces of the mean curvature flow.

Publications

Non-compactness of the space of Minimal Hypersurfaces - Math. Ann. 370 (2018), no. 1-2, 191208. 49Q05 (53A10)

Index Estimates of Self-Shrinkers in $\mathbb{R}^3$ with Asymptotically Conical Ends - Proc. Amer. Math. Soc. - https://doi.org/10.1090/proc/14306

The Width of Ellipsoids - Comm. in Analysis and Geometry, Vol.27 (2019), no.2, pp.251-285

Index Estimates for Surfaces with Constant Mean Curvature in 3-dimensional Manifolds - Calc. Var. Partial Differential Equations 60, vol. 3 (2021) (joint work with Han Hong)

Quantitative Estimates on the Singular Set of Minimal Hypersurfaces with Bounded Index - J. Geom. Anal. 34, 372 (2024) (joint work with Sean McCurdy and Paul Minter )

Compactness of the Space of Free Boundary CMC Surfaces with Bounded Topology - Geom Dedicata 219, 44 (2025) (joint work with Han Hong) (see arxiv version for correct pictures)

A Curvature Varifold Whose Weak Second Fundamental Form is Not Preserved Under Decompositions - to appear in AMPA - arxiv:2411.03684v2

Preprints

A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by C1,α Multiple Valued Functions - arxiv:2409.11861v1 (submitted)

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