GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES
Forum of Mathematics, Sigma, Tome 2 (2014)
Voir la notice de l'article provenant de la source Cambridge University Press
We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2 and higher is globally well-posed for smooth initial data as well as for initial data in certain Sobolev spaces. Thus the space of closed plane curves equipped with such a metric is geodesically complete. We find lower bounds for the geodesic distance in terms of curvature and its derivatives.
@article{10_1017_fms_2014_19,
author = {MARTINS BRUVERIS and PETER W. MICHOR and DAVID MUMFORD},
title = {GEODESIC {COMPLETENESS} {FOR} {SOBOLEV} {METRICS} {ON} {THE} {SPACE} {OF} {IMMERSED} {PLANE} {CURVES}},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {2},
year = {2014},
doi = {10.1017/fms.2014.19},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2014.19/}
}
TY - JOUR AU - MARTINS BRUVERIS AU - PETER W. MICHOR AU - DAVID MUMFORD TI - GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES JO - Forum of Mathematics, Sigma PY - 2014 VL - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2014.19/ DO - 10.1017/fms.2014.19 LA - en ID - 10_1017_fms_2014_19 ER -
%0 Journal Article %A MARTINS BRUVERIS %A PETER W. MICHOR %A DAVID MUMFORD %T GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES %J Forum of Mathematics, Sigma %D 2014 %V 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2014.19/ %R 10.1017/fms.2014.19 %G en %F 10_1017_fms_2014_19
MARTINS BRUVERIS; PETER W. MICHOR; DAVID MUMFORD. GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES. Forum of Mathematics, Sigma, Tome 2 (2014). doi: 10.1017/fms.2014.19
Cité par Sources :