Jun Michael Ling, Ph.D.

Professor

Office Hours

MW 4:00-4:50 pm. or by appointment
 

Teaching -  Spring 2013

Math 1060 Trigonometry

Math 3400 Partial Differential Equations

Research interests

Geometric analysis, Riemannian geometry, Kähler geometry, Partial differential equations. Currently I am mainly interested in research related to geometric flows, e.g., the Ricci flow.

Recent publications (2006 - )

[1] (with Xiaodong Cao, Songbo Hou)  Estimate and Monotonicity of the First Eigenvalue under Ricci Flow, Math. Ann. 354 (2012), no. 2,  451--463.

[2] (with Zhiqin Lu) Bounds of Eigenvalues on Riemannian Manifolds, Trends in Partial Differential Equations, Advanced Lectures in Mathematics 10 , editors Bian et al., International Press of Boston, 2010   (New!)

[3] (with Zhiqin Lu) Analysis and a lower bound for the first eigenvalue of a compact manifold (pdf), Preprint, 2007  (New!)

[4] Estimates on the lower bound of the first gap, Comm.  Anal. Geometry 16 (2008), no. 3, 539-563. 

[5] A comparison theorem and a sharp bound via the Ricci flow (pdf), Preprint, 2007.

[6] A class of monotonic quantities along the Ricci flow (pdf), Preprint, 2007.  

[7] An exact solution to an equation and the first eigenvalue of a compact manifold, Illinois J. Math. 51 (2007), no. 3, 853-860. 

[8] The first Dirichlet eigenvalue of a compact manifold and the Yang conjecture, Math. Nach. 280 (2007), no. 12, 1354-1362. 

[9] Lower bounds of the eigenvalues of compact manifolds with positive Ricci curvature, Ann. Glo. Anal. Geometry 31 (2007), no. 4, 385-408. 

[10] A lower bound of the first Dirichlet eigenvalue of a compact manifold with positive Ricci curvature, International J. Math. 17 (2006), no. 5, 605-617. 

[11] The first eigenvalue of a closed manifold with positive Ricci curvature, Proc. Amer. Math. Soc. 134 (2006), no. 10, 3071-3079.  

Lecture notes and others

[1] Introduction to Poincaré Conjecture, the Geometrization Conjecture of Thurston and the Ricci flow(slide presentation).

[2] Notes on Ricci Flow, Preprint (to be continued, pdf file, 111 pages,  with an appendix on principal G-bundles, classifying spaces and characteristic classes).

[3] Complex Geometry.

[4] Kähler Geometry and Kähler-Ricci Flow, Preprint (to be coninued).

Awards

UVU Board of Trustees Award of Excellence, academic year 2008 - 2009

The University of Tokyo Japanese Government Scholarship （東京大學文部省獎學金）

Workshops, talks and conferences

·Workshop in Geometric Analysis, ECNU, Shanghai, CHINA, 2008

·Recent Dev. Riem. Kaehlerian Geo., AMS Western Sec., Claremont, CA, 2008 

·Evolution Equations and Related Topics, MSRI, Berkeley, CA 

·15th SCGA, Irvine, CA

·14th SCGA, San Diego, CA 

·13th SCGA, Irvine, CA 

·Workshop in Geometry and Analysis, IMS, NJU, Nanjing, CHINA 

Links 

·AMS 

·ArXiv

·S-T Yau's recent paper on the fundamenta gap of Schrödinger operators (pdf), Matemática Contemporânea, 35 (2008) 267-285