Embeddings and immersions, Translations of Mathematical Monographs, vol.124, 1993. ,
Some applications of hölder's theorem in groups of analytic diffeomorphisms of 1-manifolds, Topology and its Applications, vol.180, pp.85-90, 2015. ,
Shape optimization by the homogenization method, Applied Mathematical Sciences, vol.146, 2002. ,
, Hyperbolic geometry. Springer Undergraduate Mathematics Series, 2005.
Condition length and complexity for the solution of polynomial systems, Found. Comput. Math, vol.16, issue.6, pp.1401-1422, 2016. ,
A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics, Arch. Ration. Mech. Anal, vol.163, issue.4, pp.259-293, 2002. ,
Differential geometry of curves and surfaces, 2016. ,
Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation ,
, Ann. Global Anal. Geom, vol.41, issue.4, pp.461-472, 2012.
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group, Ann. Global Anal. Geom, vol.44, issue.1, pp.5-21, 2013. ,
Robust certified numerical homotopy tracking, Found. Comput. Math, vol.13, issue.2, pp.253-295, 2013. ,
Matrix analysis, Graduate Texts in Mathematics, vol.169, 1997. ,
The manifold of embeddings of a closed manifold, Differential geometric methods in mathematical physics (Proc. Internat. Conf., Tech. Univ. Clausthal, vol.139, pp.310-329, 1978. ,
Déformations libres de contours pour l'optimisation de formes et application enélectromagnétisme, 2017. ,
Functional analysis, Sobolev spaces and partial differential equations, 2011. ,
Variational methods in some shape optimization problems ,
, , 2002.
Distributed control of robotic networks, Princeton Series in Applied Mathematics, 2009. ,
The geometry of geodesics, 1955. ,
The complexity of robot motion planning, ACM Doctoral Dissertation Awards, vol.1987, 1988. ,
Geodesics for a class of distances in the space of probability measures, Calc. Var. Partial Differential Equations, vol.48, issue.3-4, pp.395-420, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00686908
The action of the diffeomorphism group on the space of immersions, Differential Geom. Appl, vol.1, issue.4, pp.391-401, 1991. ,
,
Ordinary differential equations with applications, Texts in Applied Mathematics, vol.34, 2006. ,
Analytic functions and manifolds in infinite dimensional spaces ,
, North-Holland Mathematics Studies, vol.11, 1974.
Calculus on normed vector spaces, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00765800
Convexity of the geodesic distance on spaces of positive operators, Illinois J. Math, vol.38, issue.1, pp.87-94, 1994. ,
, Distance, geometry of the set of curves and optimal trajectories Bibliography
, Essential topology. Springer Undergraduate Mathematics Series, 2005.
An introduction to scientific computing, 2007. ,
Shape and topology optimization of the robust compliance via the level set method, ESAIM Control Optim. Calc. Var, vol.14, issue.1, pp.43-70, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00784065
Differential geometry of curves and surfaces, 1976. ,
Ordinary and delay differential equations, Applied Mathematical Sciences, vol.20 ,
A treatise on the differential geometry of curves and surfaces, 1960. ,
Geometry of manifolds of maps, J. Differential Geometry, vol.1, pp.169-194, 1967. ,
Translated from the Polish by K. Sieklucki, 1968. ,
Practical analysis in one variable, Undergraduate Texts in Mathematics, 2002. ,
Banach space theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 2011. ,
Topological complexity of motion planning, Discrete Comput. Geom, vol.29, issue.2, pp.211-221, 2003. ,
Invitation to topological robotics, Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), 2008. ,
Topological robotics: motion planning in projective spaces, Int. Math. Res. Not, issue.34, pp.1853-1870, 2003. ,
Curves and surfaces for computer-aided geometric design, vol.11, 1997. ,
Curves and surfaces in geometric modeling. The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling, 2000. ,
The theory of matrices. Vols. 1, 2. Translated by, 1959. ,
Diffeomorphism groups of compact convex sets, Indagationes Mathematicae, vol.28, issue.4, pp.760-783, 2017. ,
Johns Hopkins Studies in the Mathematical Sciences, 1996. ,
Adaptive subdivision and the length and energy of Bézier curves, Comput. Geom, vol.8, issue.1, pp.54-56, 1997. ,
De Casteljau's algorithm revisited, Mathematical methods for curves and surfaces, II (Lillehammer, 1997), pp.221-228, 1998. ,
Introduction to functional-differential equations, Applied Mathematical Sciences, vol.99, 1993. ,
The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.), vol.7, issue.1, pp.65-222, 1982. ,
Rings, modules and linear algebra. A further course in algebra describing the structure of Abelian groups and canonical forms of matrices through the study of rings and modules, 1970. ,
Introduction to shape optimization, Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), vol.7, 2003. ,
Introduction to matrix analysis and applications, 2014. ,
Matrix analysis, 2013. ,
Elastic shape analysis of functions, curves and trajectories, Riemannian computing in computer vision, pp.211-231, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01266838
General topology, 1955. ,
Geometric continuity of curves and surfaces, Synthesis Lectures on Visual Computing, vol.25, 2017. ,
Lectures on closed geodesics, Grundlehren der Mathematischen Wissenschaften, vol.230, 1978. ,
Foundations of differential geometry, vol.I, 1996. ,
Foundations of differential geometry, vol.II, 1996. ,
The convenient setting of global analysis, Mathematical Surveys and Monographs, vol.53, 1997. ,
Undergraduate Texts in Mathematics, 1983. ,
Differential and Riemannian manifolds, Graduate Texts in Mathematics, vol.160, 1995. ,
, Computation of normal forms and applications, vol.8, 2001.
Introduction to smooth manifolds, Graduate Texts in Mathematics, vol.218, 2013. ,
Absolute stability of nonlinear control systems, Mathematical Modelling: Theory and Applications, vol.25, 2008. ,
Time series classification with ensembles of elastic distance measures, Data Min. Knowl. Discov, vol.29, issue.3, pp.565-592, 2015. ,
Applied geometry for computer graphics and CAD, Springer Undergraduate Mathematics Series, 2005. ,
VII: The Pontryagin maximum principle, Guidance, flight mechanics and trajectory optimization, 1968. ,
Introduction to the theory of stability, Texts in Applied Mathematics, vol.24, 1987. ,
Manifolds of smooth maps. III. The principal bundle of embeddings of a noncompact smooth manifold, Cahiers Topologie Géom. Différentielle, vol.21, issue.3, pp.325-337, 1980. ,
Manifolds of differentiable mappings, Shiva Mathematics Series, vol.3, 1980. ,
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms, Doc. Math, vol.10, pp.217-245, 2005. ,
Shape optimization in fluid mechanics, Annual review of fluid mechanics, vol.36, pp.255-279, 2004. ,
Applied shape optimization for fluids. Numerical Mathematics and Scientific Computation, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00385714
Minimum variation curves and surfaces for computer-aided geometric design, Designing fair curves and surfaces, pp.123-159, 1994. ,
Mathematical biology. I, Interdisciplinary Applied Mathematics, vol.17, 2002. ,
Nonholonomic motion planning: steering using sinusoids, IEEE Trans. Automat. Control, vol.38, issue.5, pp.700-716, 1993. ,
A mathematical introduction to robotic manipulation, 1994. ,
Collisionless kinetic equations from astrophysics-the Vlasov-Poisson system, Handbook of differential equations: evolutionary equations, vol.III, pp.383-476, 2007. ,
, , pp.80008-80017
Perspectives on projective geometry, 2011. ,
Isometric immersions and embeddings of locally Euclidean metrics, Reviews in Mathematics and Mathematical Physics, vol.13, 2008. ,
Applications to computer aided geometric design, Applications of computational algebraic geometry, vol.53, pp.67-89, 1997. ,
,
Linear algebra ,
Introduction to shape optimization, Springer Series in Computational Mathematics, vol.16, 1992. ,
A comprehensive introduction to differential geometry, 1979. ,
A comprehensive introduction to differential geometry, 1979. ,
A comprehensive introduction to differential geometry, 1979. ,
A comprehensive introduction to differential geometry, 1979. ,
A comprehensive introduction to differential geometry, 1979. ,
Introduction to numerical analysis, Texts in Applied Mathematics, vol.12, 2002. ,
A combinatorial approach to planar non-colliding robot arm motion planning, 41st Annual Symposium on Foundations of Computer Science, pp.443-453, 2000. ,
Differential geometry of curves and surfaces, Pte. Ltd, 2015. ,
Chaos in electronics, of Mathematical Modelling: Theory and Applications, vol.2 ,
Nonlinear differential equations and dynamical systems ,
, ISBN 3-540-60934-2, 1996.
VI: Theory of games, astrophysics, hydrodynamics and meteorology, 1963. ,
Foundations of differentiable manifolds and Lie groups. Scott, Foresman and Co, 1971. ,
Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics, Adv. in Appl. Probab, vol.27, issue.4, pp.943-959, 1995. ,
A distance for elastic matching in object recognition, C. R. Acad. Sci. Paris Sér. I Math, vol.322, issue.2, pp.197-202, 1996. ,
Computable elastic distances between shapes, SIAM J. Appl. Math, vol.58, issue.2, pp.565-586, 1998. ,
Shapes and diffeomorphisms, Applied Mathematical Sciences, vol.171, 2010. ,