Jun Masamune

Visiting Assistant Professor
Department of Mathematical Sciences Worcester Polytechnic Institute
100 Institute Road Worcester MA 01609-2280 US
Voice: +1-508-831-5982 E-mail: masamune "at" wpi.edu

My research interests are in Geometric Analysis of manifolds, graphs, and fractal sets, and their applications to the real world problems, i.e. Math for Industry. This includes Liouville property, L^2 cohomology groups, the self adjointness of Laplacians, the conservativeness and recurrence of processes, and the convergences of energy and processes, etc. My research direction is investigation of PDEs in connection with the geometry of the underlying space.

1. The Serre duality theorem for a non-compact weighted CR manifold, joint with M. Itoh and T. Saotome. Proc. Amer. Math. Soc. 136 (2008), 3539-3548.
2. A Liouville property and its application to the Laplacian of an infinite graph. Previsional acceptance in Spectral Analysis in Geometry, Nagoya, 2007, Edited by M. Kotani, et al, Contemporary Mathematics. Amer. Math. Soc.
   
3. Vanishing and conservativeness of harmonic forms of non-compact CR manifolds. Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008), no.2, 79-102.
4. The Liouville property of unbounded fractal layers, joint with M.R. Lancia. Complex Variables and Elliptic Equations 53 (2008), no.4, 297-306
5. Conservative principle for differential forms. Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007), no.4, 351-358.
6. Essential self-adjointness of a sublaplacian via heat equation. Comm. in Partial Differential Equations, 30 (2005), no.11, 1595-1609.
7. Analysis of the Laplacian of an incomplete manifold with almost polar boundary. Rend. Mat. Appl. 25 (2005), no.1, 109-126.
8. Cauchy-Riemann orbifolds, joint with S. Dragomir. Tsukuba J. Math. 26 (2002), no.2, 351-386.
9. Discrete spectrum and Weyl's asymptotic formula for incomplete manifolds, joint with W. Rossman. Minimal surfaces, geometric analysis and symplectic geometry (Baltimore, MD, 1999), Edited by K. Fukaya, et al. 219-229, Adv. Stud. Pure Math. 34, Math. Soc. Japan, Tokyo, 2002.
10. Essential self-adjointness of Laplacians on Riemannian manifolds with fractal boundary. Comm. Partial Differential Equations, 24 (1999), no.3-4, 749-757.
11. Self-adjointness of Laplacians and conservativeness of the Brownian motion on a Riemannian manifold with fractal boundary. Ph.D Thesis, Tohoku University, Japan 1999.

1. Conservation property of a symmetric jump process, joint with T. Uemura.
2. Spherical orbits are complete, joint with M. Itoh and T. Saotome. Submitted for publication.
3. Derivation property and L^p Liouville property for non-local operators, joint with T. Uemura. Submitted for publication.
4. The Liouville property, stochastic completeness, and Stokes formulae, joint with A. Grigor'yan.
5. Vanishing theorems for harmonic forms for incomplete weighted manifolds, joint with J. Takahashi.

Invited Talks and Presentations (since 2005)

• 2008 Talk at AMS national meeting San Diego.
• 2007 Invited talk at International Conference Spectral Analysis in Geometry and Number Theory, Nagoya Japan. Invited talks at the University of Connecticut and Northeastern University.
• 2006 Invited talks at Kyoto RIMS, Tohoku University, Tokyo Institute University, Hokkaido University, Kyushu University, Tsukuba University, Okayama University, Chuo University, etc Japan.
• 2005 Lectures series Riemannian approach to fractals, the University of Rome "La Sapienza".