Brian White's Preprints


Brian White

Axial minimal surfaces in S2x R are helicoidal.
(with David Hoffman)

The maximum principle for minimal varieties of arbitrary codimension.

Sequences of embedded minimal disks whose curvatures blow up on a prescribed subset of a line.
(with David Hoffman)

On the number of minimal surfaces with a given boundary.
(with David Hoffman)

Which ambient spaces admit isopermetric inequalities for submanifolds?
J. Diff. Geom. 83 (2009), 213-228. arXiv

Currents and flat chains associated to varifolds, with an application to mean curvature flow.
Duke Math. J. 148 (2009), no. 1, 41-62. arXiv

The geometry of genus-one helicoids.
(with David Hoffman)
Comm. Math. Helv. 84 (2009), no. 3, 547-569. arXiv

Genus-one helicoids from a variational point of view.
(with David Hoffman)
Comm. Math. Helv. 83 (2008), no. 4, 767-813. arXiv

Evolution of curves and surfaces by mean curvature.
Proceedings of the International Congress of Mathematicians, Vol I (Beijing, 2002), 525-538.
arXiv, postscript file.

Embeddedness of minimal surfaces with total boundary curvature at most 4&pi.
(with Tobias Ekholm and Daniel Wienholtz)
Annals of Mathematics. 155 (2002), no. 1, 109-234.
arXiv, abstract , dvi, ps.

A local regularity theorem for mean curvature flow.
Ann. of Math. 161 (2005), 148-1519.
abstract , pdf, dvi, ps.

The nature of singularities in mean curvature flow of mean convex surfaces.
Journal of the Amer. Math. Soc. 16 (2003), 123-138.
jams link, abstract , pdf, dvi, ps.

The size of the singular set in mean curvature flow of mean convex surfaces.
Journal of the Amer. Math. Soc. 13 (2000), no. 3, 665-695.
free from JAMS. abstract , dvi, ps.

The deformation theorem for flat chains.
Acta Mathematica 183 (1999), no. 2, 255-271.
abstract , dvi, pdf (acrobat), ps.

Rectifiability of flat chains.
Annals of Mathematics 150 (1999), no. 1, 165-184.
published paper on jstor, abstract , dvi, ps.

The mathematics of F. J. Almgren, Jr.
J. Geom. Analysis 8 (1998), no. 5, 681--702.(to appear)
pdf (adobe acrobat; 275 kb), dvi (110 kb), ps.
A condensed verion appeared in the Notices of the Amer. Math. Soc. 44(11), 1451--1456. The condensed version is available from the online AMS Notices.

Soap-films bounded by non-closed curves.
(with J. Drachman) J. Geom. Analysis 8 (1998), no. 2, 239-250.
abstract , paper .

Classical area minimizing surfaces with real analytic boundaries.
Acta Mathematica 179 (1997), no. 2, 295-305.
abstract , AMS-TeX, dvi, ps.

Stratification of minimal surfaces, mean curvature flows, and harmonic maps.
J. Reine und Angewandte Math. 488 (1997), pages 1-35.
abstract , dvi, ps;
Figures (.gif): 1, 2, 3.

Half of enneper's surface minimizes area.
"Geometric analysis and the calculus of variations for Stefan Hildebrandt", pages 361-368
(International Press 1996, ed. J. Jost.)
abstract , AMS-TeX, dvi, ps.

Existence of least-energy configurations of immiscible fluids.
J. Geom. Analysis 6 (1996), 151-161.
abstract , AMS-TeX, dvi, ps.

The topology of hypersurfaces moving by mean curvature
Communications in Analysis and Geometry 3 (1995), 317-333.

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