Full-time Faculty
Photo of Duy-Minh Nhieu
Professor & Vice Chair

Duy-Minh Nhieu

Research areas

  • Geometry analysis
  • Real analysis

Education

Ph.D., Purdue University

Experience

2009/08 ~ Professor, National Central University
2008/01 ~ 2009/05 Associate Professor, San Diego Christian College
2000/08 ~ 2007/12 Assistant Professor, Georgetown University
1996/12 ~ 2000/07 Assistant Research Fellow, Institute of Mathmatics, Academia Sinica

Honors

1. 國家理論科學中心98-99學年度「中心科學家」 
 

Publications

  1. joint with D. Danielli, N. Garofalo Sub-Riemannian Calculus and monotonicity of the perimeter for graphical strips,Math Z., Published online 21 April , 2009.
  2. (with Danielli, D.; Garofalo, N.; Pauls, S. D.) Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group $\Bbb H\sp 1$. J. Differential Geom. 81 (2009), no. 2, 251--295.
  3. joint with L. Capogna and N. Garofalo Mutual absolute continuity of harmonic andsurface measures for Hormander type operators Perspectives in Partial Differential Equations, Harmonic Analysis and Applications. In honor of Vladimir Maz'ya’s 70th birthday, 49--100, Proc. Sympos. Pure Math., 79, Amer. Math. Soc., Providence, RI, 2008.
  4. (with Danielli, D.; Garofalo, N.) A notable family of entire intrinsic minimal graphs in the Heisenberg group which are not perimeter minimizing. Amer. J. Math. 130 (2008), no. 2, 317--339.
  5. (with Danielli, Donatella; Garofalo, Nicola) A partial solution of the isoperimetric problem for the Heisenberg group. Forum Math. 20 (2008), no. 1, 99--143.
  6. (with Danielli, D.; Garofalo, N.) Sub-Riemannian calculus on hypersurfaces in Carnot groups. Adv. Math. 215 (2007), no. 1, 292--378.
  7. (with Danielli, Donatella; Garofalo, Nicola) Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Caratheodory spaces. Mem. Amer. Math. Soc. 182 (2006), no. 857, x+119 pp.
  8. (with Chang, Der-Chen; Chang, Eric C.; Fan, Haitao) Mathematical analysis of the two-color partial rainbow options. Appl. Anal. 84 (2005), no. 7, 737--757.
  9. (with Danielli, D.; Garofalo, N.; Tournier, F.) The theorem of Busemann-Feller-Alexandrov in Carnot groups. Comm. Anal. Geom. 12 (2004), no. 4, 853--886.
  10. (with Chang, Der-Chen) A difference equation arising from logistic population growth. Appl. Anal. 83 (2004), no. 6, 579--598.
  11. (with Danielli, Donatella; Garofalo, Nicola) Notions of convexity in Carnot groups. Comm. Anal. Geom. 11 (2003), no. 2, 263--341.
  12. (with Danielli, Donatella; Garofalo, Nicola) On the best possible character of the $L\sp Q$ norm in some a priori estimates for non-divergence form equations in Carnot groups. Proc. Amer. Math. Soc. 131 (2003), no. 11, 3487--3498
  13. (with Capogna, Luca; Garofalo, Nicola) Properties of harmonic measures in the Dirichlet problem for nilpotent Lie groups of Heisenberg type. Amer. J. Math. 124 (2002), no. 2, 273--306.
  14. The Neumann problem for sub-Laplacians on Carnot groups and the extension theorem for Sobolev spaces. Ann. Mat. Pura Appl. (4) 180 (2001), no. 1, 1--25.
  15. (with Danielli, Donatella; Garofalo, Nicola) Sub-elliptic Besov spaces and the characterization of traces on lower dimensional manifolds. Harmonic analysis and boundary value problems (Fayetteville, AR, 2000), 19--37, Contemp. Math., 277, Amer. Math. Soc., Providence, RI, 2001.
  16. (with Capogna, Luca; Garofalo, Nicola) Examples of uniform and NTA domains in Carnot groups. Proceedings on Analysis and Geometry (Russian) (Novosibirsk Akademgorodok, 1999), 103--121, Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 2000.
  17. (with Danielli, Donatella; Garofalo, Nicola) Trace inequalities for Carnot-Caratheodory spaces and applications. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 27 (1998), no. 2, 195--252 (1999).
  18. (with Capogna, Luca; Garofalo Nicola) A version of a theorem of Dahlberg for the subelliptic Dirichlet problem. Math. Res. Lett. 5 (1998), no. 4, 541--549.
  19. (with Danielli, Donatella; Garofalo, Nicola) Isoperimetric and trace inequalities with respect to Carnot-Caratheodory metrics. Geometry Seminars, 1996--1997 (Italian) (Bologna), 51--62, Univ. Stud. Bologna, Bologna, 1998.
  20. (with Garofalo, Nicola) Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Caratheodory spaces. J. Anal. Math. 74 (1998), 67--97.
  21. (with Garofalo, Nicola) Isoperimetric and Sobolev inequalities for Carnot-Caratheodory spaces and the existence of minimal surfaces. Comm. Pure Appl. Math. 49 (1996), no. 10, 1081--1144.
  22. Extension of Sobolev spaces on the Heisenberg group. C. R. Acad. Sci. Paris Ser. I Math. 321 (1995), no. 12, 1559--1564.