scholarly journals Quasiregular mappings and 𝒲𝒯 -classes of differential forms on Riemannian manifolds

2002 â—˝  
Vol 202 (1) â—˝  
pp. 73-92 â—˝  
Author(s):  
D. Franke â—˝  
O. Martio â—˝  
V.M. Miklyukov â—˝  
M. Vuorinen â—˝  
R. Wisk
Keyword(s):  
Riemannian Manifolds â—˝  
Differential Forms â—˝  
Quasiregular Mappings

scholarly journals Solving Liouville-type Problems on Manifolds with Poincaré-Sobolev Inequality by Broadening q-Energy from Finite to Infinite

10.5539/jmr.v9n4p1 â—˝  
2017 â—˝  
Vol 9 (4) â—˝  
pp. 1
Author(s):  
Lina Wu
Keyword(s):  
Riemannian Manifolds â—˝  
Sobolev Inequality â—˝  
Differential Forms â—˝  
Computational Method â—˝  
Liouville Type â—˝  
Balanced Growth â—˝  
Curved Manifolds â—˝  
Research Findings â—˝  
Liouville Type Results â—˝  
Flat Manifolds

The aim of this article is to investigate Liouville-type problems on complete non-compact Riemannian manifolds with Poincaré-Sobolev Inequality. Two significant technical breakthroughs are demonstrated in research findings. The first breakthrough is an extension from non-flat manifolds with non-negative Ricci curvatures to curved manifolds with Ricci curvatures varying among negative values, zero, and positive values. Poincaré-Sobolev Inequality has been applied to overcome difficulties of an extension on manifolds. Poincaré-Sobolev Inequality has offered a special structure on curved manifolds with a mix of Ricci curvature signs. The second breakthrough is a generalization of $q$-energy from finite to infinite. At this point, a technique of $p$-balanced growth has been introduced to overcome difficulties of broadening from finite $q$-energy in $L^q$ spaces to infinite $q$-energy in non-$L^q$ spaces. An innovative computational method and new estimation techniques are illustrated. At the end of this article, Liouville-type results including vanishing properties for differential forms and constancy properties for differential maps have been verified on manifolds with Poincaré-Sobolev Inequality approaching to infinite $q$-energy growth.

scholarly journals Complex-valued differential forms on normal contact Riemannian manifolds

1966 â—˝  
Vol 18 (4) â—˝  
pp. 349-361 â—˝  
Author(s):  
Tamehiro Fujitani
Keyword(s):  
Riemannian Manifolds â—˝  
Differential Forms â—˝  
Normal Contact â—˝  
Complex Valued

Boundary value problems for differential forms on compact Riemannian manifolds, Part II

Analysis â—˝  
2007 â—˝  
Vol 27 (4) â—˝  
Author(s):  
Jürgen Bolik
Keyword(s):  
Boundary Value Problems â—˝  
Riemannian Manifolds â—˝  
Boundary Value â—˝  
Differential Forms â—˝  
Second Order â—˝  
First Order

SummaryThis paper provides solutions to second order boundary value problems for differential forms by means of the method applied in [3] for first order problems. These

Differential forms on riemannian manifolds

1955 â—˝  
Vol 8 (4) â—˝  
pp. 551-590 â—˝  
Author(s):  
K. O. Friedrichs
Keyword(s):  
Riemannian Manifolds â—˝  
Differential Forms

scholarly journals $\bar{WT}$-Classes of Differential Forms on Riemannian Manifolds

2008 â—˝  
Vol 48 (1) â—˝  
pp. 73-79
Author(s):  
Gao Hongya â—˝  
Gu Zhihua â—˝  
Chu Yuming
Keyword(s):  
Riemannian Manifolds â—˝  
Differential Forms
Sign in / Sign up

Export Citation Format

Share Document