** Professor of Mathematics **

*Research Interests: *Geometric measure theory, partial differential equations, differential geometry

## Publications

Fine properties of branch point singularities: stationary two-valued
graphs and stable minimal hypersurfaces near points of density $< 3$

(2021)

A Structure Theory for Stable Codimension 1 Integral Varifolds with
Applications to Area Minimising Hypersurfaces mod p

(2021)

Stable prescribed-mean-curvature integral varifolds of codimension 1: regularity and compactness

(2019)

Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces

– Advances in Mathematics

(2018)

352,

133

(DOI: 10.1016/j.aim.2019.05.023)

Stable CMC integral varifolds of codimension $1$: regularity and
compactness

(2018)

Fine properties of branch point singularities: Dirichlet energy
minimizing multi-valued functions

(2017)

Regularity and compactness for stable codimension $1$ CMC varifolds

– Current Developments in Mathematics

(2017)

2017,

87

(DOI: 10.4310/cdm.2017.v2017.n1.a3)

A Frequency Function and Singular Set Bounds for Branched Minimal Immersions

– Communications on Pure and Applied Mathematics

(2016)

69,

1213

(DOI: 10.1002/cpa.21642)

The Blow Up Method for Brakke Flows: Networks Near Triple Junctions

– Archive for Rational Mechanics and Analysis

(2016)

221,

1161

(DOI: 10.1007/s00205-016-0981-3)

Regularity of stable minimal hypersurfaces: Recent advances in the theory and applications

– Journal of Differential Geometry

(2015)

19,

231

(DOI: 10.4310/sdg.2014.v19.n1.a9)

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