Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Entire DC Network
Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani
Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani
Faculty Research and Creative Activity
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F. If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established.
Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani
Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani
Faculty Research and Creative Activity
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F. If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established.
A Tikz Tutorial: Generating Graphics In The Spirit Of Tex, Andrew Mertz, William Slough
A Tikz Tutorial: Generating Graphics In The Spirit Of Tex, Andrew Mertz, William Slough
Faculty Research and Creative Activity
TikZ is a system which can be used to specify graphics of very high quality. For example, accurate place- ment of picture elements, use of TEX fonts, ability to incorporate mathematical typesetting, and the possi- bility of introducing macros can be viewed as positive factors of this system. The syntax uses an amal- gamation of ideas from METAFONT, METAPOST, PSTricks, and SVG, allowing its users to \program" their desired graphics. The latest revision to TikZ introduces many new features to an already feature- packed system, as evidenced by its 560-page user manual. Here, we present a tutorial overview of this …