JAMP  Vol.3 No.7 , July 2015
New Model for L2 Norm Flow
Abstract: We introduce a new L2 norm preserving heat flow in matrix geometry. We show that this flow exists globally and preserves the positivity property of Hermitian matrices.
Cite this paper: Li, J. and Dou, M. (2015) New Model for L2 Norm Flow. Journal of Applied Mathematics and Physics, 3, 741-745. doi: 10.4236/jamp.2015.37089.

[1]   Duvenhage, R. (2014) Noncommutative Ricci flow in a Matrix Geometry. Journal of Physics A: Mathematical and Theoretical, 47, 045203.

[2]   Hamilton, R. (1988) The Ricci Flow on Surfaces. Mathematics and General Relativity: Proceedings of the AMS-CIMS- CSIAM Joint Summer Research Conference, Contemporary Mathematics, 71, 237-262. (Providence, RI: American Mathematical Society.

[3]   Dai, X. and Ma, L. (2007) Mass under Ricci Flow. Communications in Mathematical Physics, 274, 65-80.

[4]   Li, J.J. (2015) Heat Equation in a Model Matrix Geometry. C. R. Acad. Sci. Paris, Ser. I.

[5]   Caffarelli, L. and Lin, F.H. (2009) Non-Local Heat Flows Preserving the L2 Energy. Discrete Contin. Dynam. Syst., 23, 49-64.

[6]   Ma, L. and Cheng, L. (2009) Non-Local Heat Flows and Gradient Estimates on Closed Manifolds. Journal of Evolution Equations, 9, 787-807.

[7]   Ma, L. and Cheng, L. (2013) A Non-Local Area Preserving Curve Flow. Geometriae Dedicata, 171, 231-247.

[8]   Ma, L. and Zhu, A.Q. (2012) On a Length Preserving Curve Flow. Monatshefte für Mathematik, 165, 57-78.

[9]   Li, B., Yu, Z.H., Fei, S.M. and Li-Jost, X.Q. (2013) Time Optimal Quantum Control of Two-Qubit Systems. Science China Physics, Mechanics and Astronomy, 56, 2116-2121.

[10]   Nielsen, M.A. and Chuang, I.L. (2004) Quantum computation and Quantum Information. Cambridge Univ. Press, Cambridge.

[11]   Connes, A. (1994) Noncommutative Geometry. Aca-demic Press.

[12]   Madore, J. (1999) An Introduction to Noncommutative Differential Geometry and Its Physical Applications. 2nd Edition, Cambridge University Press, Cambridge.