Welcome to Robert Hardt's Home Page

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.

Research Interests

Graduate Students,

Recent Papers

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 W22(B5,S3) * (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.


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