Sharp constants for composition with a bi-Lipschitz measure-preserving map
نویسندگان
چکیده
منابع مشابه
What Happens to a Manifold Under a Bi-Lipschitz Map?
We study geometric and topological properties of the image of a smooth submanifold of Runder a bi-Lipschitz map to R. In particular, we characterize how the dimension, diameter,volume, and reach of the embedded manifold relate to the original. Our main result establishesa lower bound on the reach of the embedded manifold in the case where m ≤ n and the bi-Lipschitz map is li...
متن کاملVolume Preserving Bi-lipschitz Homeomorphisms on the Heisenberg Group
The use of sub-Riemannian geometry on the Heisenberg group H(n) provides a compact picture of symplectic geometry. Any Hamiltonian diffeomorphism on R lifts to a volume preserving bi-Lipschitz homeomorphisms of H(n), with the use of its generating function. Any curve of a flow of such homeomorphisms deviates from horizontality by the Hamiltonian of the flow. From the metric point of view this m...
متن کاملLipschitz Extension Constants Equal Projection Constants
For a Banach space V we define its Lipschitz extension constant, LE(V ), to be the infimum of the constants c such that for every metric space (Z, ρ), every X ⊂ Z, and every f : X → V , there is an extension, g, of f to Z such that L(g) ≤ cL(f), where L denotes the Lipschitz constant. The basic theorem is that when V is finite-dimensional we have LE(V ) = PC(V ) where PC(V ) is the well-known p...
متن کاملBi-Lipschitz Decomposition of Lipschitz functions into a Metric space
We prove a quantitative version of the following statement. Given a Lipschitz function f from the k-dimensional unit cube into a general metric space, one can be decomposed f into a finite number of BiLipschitz functions f |Fi so that the k-Hausdorff content of f([0, 1] r ∪Fi) is small. We thus generalize a theorem of P. Jones [Jon88] from the setting of R to the setting of a general metric spa...
متن کاملLipschitz Constants to Curve Complexes
We determine the asymptotic behavior of the optimal Lipschitz constant for the systole map from Teichmüller space to the curve complex.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2014
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2014.v21.n5.a2