A note on harmonic maps between surfaces
A note on heat kernel estimates on weighted graphs with two-sided bounds on the weights.
A note on intermediate differentiability of Lipschitz functions
Let be a Lipschitz function on a superreflexive Banach space . We prove that then the set of points of at which has no intermediate derivative is not only a first category set (which was proved by M. Fabian and D. Preiss for much more general spaces ), but it is even -porous in a rather strong sense. In fact, we prove the result even for a stronger notion of uniform intermediate derivative which was defined by J.R. Giles and S. Sciffer.
A note on n-ary Poisson brackets
An -ary Poisson bracket (or generalized Poisson bracket) on the manifold is a skew-symmetric -linear bracket of functions which is a derivation in each argument and satisfies the generalized Jacobi identity of order , i.e.,
A note on quasilinear elliptic eigenvalue problems.
A note on Ricci flow and optimal transportation
We describe a new link between Perelman’s monotonicity formula for the reduced volume and ideas from optimal transport theory.
A Note on Right-Equivalence of Map-Germs.
A note on singular points of convex functions in Banach spaces
A note on strong differentiability spaces
A note on strong resonance problems for -Laplacian.
A Note on Sufficiency of Jets.
A note on tangent bundles in a category with a ring object.
A Note on the Alexander Theorem on the Complex Plane
We investigate the Banach manifold consisting of complex functions on the unit disc having boundary values in a given one-dimensional submanifold of the plane. We show that ∂/∂λ̅ restricted to that submanifold is a Fredholm mapping. Moreover, for any such function we obtain a relation between its homotopy class and the Fredholm index.
A note on the existence of two nontrivial solutions of a resonance problem.
A Note on the First Nonzero Eigenvalue of the Laplacian Acting of P-Forms.
A note on the holonomy of connections in twisted bundles
A note on the inverse function theorem of Nash and Moser.
A note on the isoperimetric constant
A Note on the Order of Determination of a Finitely Determined Germ.
A note on trignometric sums arising in gauge theory.