Search results for "Flat torus"
showing 3 items of 3 documents
Large data scattering for NLKG on waveguide ℝd × 𝕋
2020
We consider the pure-power defocusing nonlinear Klein–Gordon equation, in the [Formula: see text]-subcritical case, posed on the product space [Formula: see text], where [Formula: see text] is the one-dimensional flat torus. In this framework, we prove that scattering holds for any initial data belonging to the energy space [Formula: see text] for [Formula: see text]. The strategy consists in proving a suitable profile decomposition theorem on the whole manifold to pursue a concentration-compactness and rigidity method along with the proofs of (global in time) Strichartz estimates.
Torus computed tomography
2020
We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization problem associated to Tikhonov regularization in Sobolev spaces and prove that the solution operator provides an admissible regularization strategy with a quantitative stability estimate. This regularization is a simple post-processing low-pass filter for the Fourier series of a phantom. We also study the adjoint and the normal operator of the X-ray transform on the flat torus. The X-ray transform is unitary on the flat torus. We have i…
Volume preserving mean curvature flows near strictly stable sets in flat torus
2021
In this paper we establish a new stability result for the smooth volume preserving mean curvature flow in flat torus $\mathbb T^n$ in low dimensions $n=3,4$. The result says roughly that if the initial set is near to a strictly stable set in $\mathbb T^n$ in $H^3$-sense, then the corresponding flow has infinite lifetime and converges exponentially fast to a translate of the strictly stable (critical) set in $W^{2,5}$-sense.