My research interests are in Geometric Analysis of Riemannian manifolds, CR manifolds, graphs, fractal sets, and its applications to the real world problems. This includes Liouville property, L^2 cohomology groups, the self adjointness of Laplacians, the conservativeness and recurrence of processes, the convergences of energy and processes, and the homogenization theory. My research direction is investigation of PDEs in connection with the geometry of the underlying space.
Publications and preprints
X.-P. Huang, M. Keller, J. Masamune, R.-K. Wojciechowski, A note on self-adjoint extensions of the Laplacian on weighted graphs, preprint, 2012, 16 pages (PDF@arXiv).
- A. Grigor'yan, J. Masamune, Parabolicity and Stochastic completeness of manifolds in terms of Green formula, to appaer in Journal de MatheLmatiques Pures et AppliqueLes, 29 pages (PDF).
- J. Masamune, T. Uemura, J. Wang, On the conservativeness and recurrence of symmetric jump-diffusions, J. Funct. Anal., 263 (2012), no. 12, 3984-4008 (PDF).
- A. Grigor'yan, X.-P. Huang, J. Masamune, On stochastic completeness of jump processes, Math Z. 271 (2012), no. 3-4, 1211-1239 DOI: 10.1007/s00209-011-0911-x. 29 pages, (PDF).
- J. Masamune, On a stability of essential spectra of Laplacians under non-compact change of metric,
Proc. Amer. Math. Soc. 140 (2012), 1045-1052.
DOI: 10.1090/S0002-9939-2011-10965-1, (PDF).
- J. Masamune, T. Uemura, L^p Liouville property of non-local operators, Math. Nachr. 284 (2011), no. 17-18, 2249-2267, DOI: 10.1002/mana.200910211 (PDF).
- J. Masamune, The Mosco convergence and the weak convergence of Wiener measures for conductive thin boundaries, J. Math. Anal. Appl. 384 (2011), no. 2, 504|526. DOI: 10.1016/j.jmaa.2011.06.004.
- J. Masamune, T. Uemura, Conservation property of symmetric jump processes, Ann. Inst. Henri Poincare Probab. Stat, 47 (2011) no. 3, 650-662 DOI: 10.1214/09-AIHP368, (PDF).
- J. Masamune, A Liouville property and its application to the Laplacian of an infinite graph. Spectral analysis in geometry and number theory, 103-115, Papers from the International Conference on the occasion of Toshikazu Sunada's 60th birthday held at Nagoya University, Nagoya, August 6-10, 2007. Edited by Motoko Kotani, et al Contemp. Math., 484, Amer. Math. Soc., Providence, RI, 2009, (PDF).
- M. Itoh, J. Masamune, T. Saotome, The Serre duality theorem for a non-compact weighted CR manifold, Proc. Amer. Math. Soc. 136 (2008), no. 10, 3539--3548, (PDF).
- J. Masamune, Vanishing and conservativeness of harmonic forms of a noncompact CR manifold, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008), no. 2, 79-102.
- J. Masamune, M.R. Lancia, The Liouville property of unbounded fractal layers, Complex Var. Elliptic Equ. 53 (2008), no. 4, 297--306.
- J. Masamune, Conservative principle for differential forms, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007), 351-358.
- J. Masamune, Essential self-adjointness of a sublaplacian via heat equation, Comm. in Partial Differential Equations, 30 (2005), no.11, 1595-1609.
- J. Masamune, Analysis of the Laplacian of an incomplete manifold with almost polar boundary, Rend. Mat. Appl. 25 (2005), no.1, 109-126.
- S. Dragomir, J. Masamune, Cauchy-Riemann orbifolds, Tsukuba J. Math. 26 (2002), no.2, 351-386.
- J. Masamune, W. Rossman, Discrete spectrum and Weyl's asymptotic formula for incomplete manifolds, 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, (PDF).
- J. Masamune, Essential self-adjointness of Laplacians on Riemannian manifolds with fractal boundary, Comm. in Partial Differential Equations, 24 (1999), no.3-4, 749-757.
J. Masamune, Hiring and research funding systems of Italian Mathematical Society (in Japanese), Sugaku Tushin, 10 (2005) no 3, 58-61, (PDF).
J. Masamune, Self-adjointness of Laplacians and conservativeness of the Brownian motion on a Riemannian manifold with fractal boundary. Ph.D. Thesis, Tohoku University, Sendai Japan 1999.
- J. Masamune, Professional Science Master's, an innovative new graduate degree in the United States (in Japanese), Sugaku Tushin, 16 (2011) no. 2, 22-30, (PDF). Related information to this article can be found at
Invited talks, presentations, and professional meetings (since 2005)
- University of Jena, Germany
- PSU, University Park
- CUNY Graduate Center
- Cornell University
- PSU, Altoona and UP
- CUNY Graduate Center
- University of Bielefeld, Germany May - June
- University of Jena, Germany
- TD Dresden, Germany.
- International workshop Operators on Singular spaces, March, Potsdam Germany.
- Rome University ``La Sapienza'' MeMoMat, March, Rome Italy.
- Rome University ``La Sapienza'' Italy, May-July, Germany.
- University of Bielefeld, May - July, Germany.
- Fourth international conference on stochastic analysis and its application, September.
- Lecture series, Kyoto University (GCOE), Thanksgiving break.
- Mathematics Colloquium Talk, Penn State Altoona, Nov, PA USA.
- Workshop Differential Equations on Manifolds, Oct, Toyama, Japan.
- AMS 2009 Fall Eastern Meeting Pennsylvania State University Microlocal Analysis and Spectral Theory on Singular Spaces, Oct, PA USA.
- Kyoto University, Aug, Kyoto Japan.
- AMS 2009 Spring Eastern Meeting MA Special Session on Scaling, Irregularities, and Partial Differential Equations, March, MA USA.
- International workshop Partial Differential Equations and Applications in Geometry, March, Konstanz Germany.
- Workshop Riemannian Geometry and Geometric Analysis, Jan, Tsukuba Japan.
- International workshop Computer Algebra, Jan, Kobe Japan.
- Colloquium Talk, Penn State Altoona, Jan, PA USA.
2008 AMS national meeting San Diego, Jan, CA USA.
- 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".
Penn State Altoona
115B Smith Building, 3000 Ivyside Park, Altoona, Pennsylvania 16601 US
E-mail: jum35 "at" psu.edu
|Copyright © 2012, Penn State Altoona
All rights reserved