** Professor of Mathematics **

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

## Publications

Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces

– Advances in Mathematics

(2019)

352,

133

(DOI: 10.1016/j.aim.2019.05.023)

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

(2014)

19,

231

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

A general regularity theory for stable codimension 1 integral varifolds

– Annals of Mathematics

(2014)

179,

843

(DOI: 10.4007/annals.2014.179.3.2)

Fine properties of branch point singularities: Two-valued harmonic
functions

– arXiv:1311.0923

A sharp strong maximum principle and a sharp unique continuation theorem for singular minimal hypersurfaces

– Calculus of Variations and Partial Differential Equations

(2014)

51,

799

(DOI: 10.1007/s00526-013-0695-4)

Stable phase interfaces in the van der Waals--Cahn--Hilliard theory

– Journal für die reine und angewandte Mathematik (Crelles Journal)

(2012)

2012,

191

(DOI: 10.1515/crelle.2011.134)

A regularity and compactness theory for immersed stable minimal hypersurfaces of multiplicity at most 2

– J DIFFER GEOM

(2008)

80,

79

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