15 papers
A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions
Károly J. Böröczky, Alessio Figalli, João P. G. Ramos
We prove that if a triplet of functions satisfies almost equality in the Prékopa-Leindler inequality, then these functions are close to a common log-concave function, up to multipl…
Uniqueness of solutions to nonlinear Schrödinger equations from their zeros
Christoph Kehle, João P. G. Ramos
We show novel types of uniqueness and rigidity results for Schrödinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result w…
Uniform bounds for oscillatory and polynomial Carleson operators
João P. G. Ramos
We prove that a variety of oscillatory and polynomial Carleson operators are uniformly bounded on the family of parameters under considerations. As a particular application of our…
Bounds for the Lonely Runner Problem via Linear Programming
Felipe Gonçalves, João P. G. Ramos
In this note we develop a linear programming framework to produce upper and lower bounds for the lonely runner problem.
Maximal function estimates and local well-posedness for the generalized Zakharov--Kuznetsov equation
Felipe Linares, João P. G. Ramos
We prove a high-dimensional version of the Strichartz estimates for the unitary group associated to the free Zakharov--Kuznetsov equation. As a by--product, we deduce maximal estim…
The Cauchy problem for the critical generalized Zakharov-Kuznetsov equation in dimension 3
Felipe Linares, João P. G. Ramos
We prove local well-posedness for the critical generalized Zakharov-Kuznetsov equation in We also prove that the equation is "almost well-posedness"…