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, differential geometry and applications.
I previously held postdoctoral positions at University of Toronto, University of British Columbia and Lecturer (fixed-term) at University of Auckland
CV (Feb 2026)
Brief Research Summary
My research area lies in the intersection of Geometric Measure Theory, Analysis and Calculus of Variations.
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.
Currently I have also been interested in Almgren's multiple-valued functions and its applications to high codimension submanifolds.
Publications
A Curvature Varifold Whose Weak Second Fundamental Form is Not Preserved Under Decompositions - Annali di Matematica (2025) - https://doi.org/10.1007/s10231-025-01601-z
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)
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 )
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)
The Width of Ellipsoids - Comm. in Analysis and Geometry, Vol.27 (2019), no.2, pp.251-285
Index Estimates of Self-Shrinkers in $\mathbb{R}^3$ with Asymptotically Conical Ends - Proc. Amer. Math. Soc. - https://doi.org/10.1090/proc/14306
Non-compactness of the space of Minimal Hypersurfaces - Math. Ann. 370 (2018), no. 1-2, 191208. 49Q05 (53A10)
Preprints
Quantitative Estimates on the Topology and Singular Set of Prescribed Mean Curvature Hypersurfaces - submitted - arXiv:2602.19804 (joint work with Sean McCurdy and Paul Minter )
A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by C1,α Multiple Valued Functions - arxiv:2409.11861v1 (submitted)