Robert Hardt

Dept. of Mathematics

Rice University

P.
O. Box 1892

Houston, TX 77251

Tel. (713) 348-3280

Math. Dept. (713) 527-4829

Fax. (713)
285-5231

W.L.Moody Professor

B.S.(1967) Massachusetts Institute of
Technology; Ph.D.(1971)Brown University.

Geometric measure theory, partial differential equations, continuum mechanics.

*Review
of Constant Mean CurvatureSurfaces, Harmonic Maps, and Integrable
Systems* *by Frederic Helein*** Bull.Amer.Math.Soc.
***40**(1)(2003), pp. 12-123.

*Size
minimization and approximating problems.** (with T. De Pauw)
*Calculus of Variations PDE ***17** (2003)(4), pp. 405-442.

*Connecting
Topological Hopf Singularities*.* (with Tristan Riviere)
*Annali* *Sc.Norm.SupPisa*.**II**(2003),
pp. 287-344.

*Singular
sets of higher order equations*.*
(with F.Lin and Q.Han) *Comm.P.D.E*. **28**(2003), no.11-12,
pp. 2045-2063.

*Applications
of Scans and Fractional Power Integrands* *(with T. De Pauw),
in *Variational Problems in Riemannian Geometry, *Progress in
Nonlinear Differential Equations and Their Applications 59,
Birkhauser, Basel, 2004, pp.19-32.

Editted *Six Themes on Variation*, Student Mathematical
Library **26**, Amer. Math.Soc, Providence, 2004.

Connecting Rational Homotopy Type Singularities * (with Tristan Riviere). 64pp.,Submitted, 2005.

Convergence on manifolds of Gibbs measures which are absolutely continuous with respect to Hausdorff measures * (with D.Cox and P.Kloucek) 21pp.2005.

Bubbling
Phenomena and Weak Convergence for Maps in W^{22}(B^{5},S^{3})
* (with Tristan Riviere). Incomplete preliminary version,22pp.

*Research supported by NSF grant DMS-0306294

**Course Homepages**

Math 521, Fall 2001, Advanced Topics in Real Analysis

Math 426, Spring 2002, Topics in Real Analysis

Math 521, Fall 2002, Advanced Topics in Real Analysis

Math 522, Spring 2003, Advanced Topics in Real Analysis

Math 401, Fall 2003, Differential Geometry

Math 402, Spring 2004, Differential Geometry

Math 521, Fall 2004, Advanced Topics in Real Analysis

Math 425, Fall 2005, Integration Theory

Math 424, Spring 2007, Partial Differential Equations

Math 522, Spring 2007, Advanced Topics in Real Analysis

Math 423,Fall 2008, Partial Differential Equations

Math 521, Fall 2008, Advanced Topics in Real Analysis (Functions of Bounded Variation)

Math 498,698 Research Themes in the Mathematical Sciences, (Imaging)

Some analysis preliminary exams and their solutions.