On the 1/H1/H-flow by pp-Laplace approximation: new estimates via fake distances under Ricci lower bounds

In this paper we show the existence of weak solutions $w : M \rightarrow \mathbb{R}$ of the inverse mean curvature flow starting from a relatively compact set (possibly, a point) on a large class of manifolds satisfying Ricci lower bounds. Under natural assumptions, we obtain sharp estimates for the growth of $w$ and for the mean curvature of its level sets, that are well behaved with respect to Gromov-Hausdorff convergence. The construction follows R. Moser's approximation procedure via the $p$-Laplace equation, and relies on new gradient and decay estimates for $p$-harmonic capacity potentials, notably for the kernel $\mathcal{G}_p$ of $\Delta_p$. These bounds, stable as $p \rightarrow 1$, are achieved by studying fake distances associated to capacity potentials and Green kernels. We conclude by investigating some basic isoperimetric properties of the level sets of $w$.Comment: 61 pages. Revised version. Section 3.2 (properness under volume doubling and weak Poincar\'e inequalities, p.41-45) was rewritten, and the main Theorems 1.4 and 4.6 changed accordingl

e-{\mu} Discrimination at High Energy in the JUNO Detector

Cosmic Ray and neutrino oscillation physics can be studied by using atmospheric neutrinos. JUNO (Jiangmen Underground Neutrino Observatory) is a large liquid scintillator detector with low energy detection threshold and excellent energy resolution. The detector performances allow the atmospheric neutrino oscillation measurements. In this work, a discrimination algorithm for different reaction channels of neutrino-nucleon interactions in the JUNO liquid scintillator, in the GeV/sub-GeV energy region, is presented. The atmospheric neutrino flux is taken as reference, considering $\overset{(-)}{\nu_\mu}$ and $\overset{(-)}{\nu_e}$. The different temporal behaviour of the classes of events have been exploited to build a time profile-based discrimination algorithm. The results show a good selection power for $\overset{(-)}{\nu_e}$ CC events, while the $\overset{(-)}{\nu_\mu}$ CC component suffers of an important contamination from NC events at low energy, which is under study. Preliminary results are presented.Comment: Proceeding for poster presented at the 7th Roma International Conference on AstroParticle Physic

Remarks on mean curvature flow solitons in warped products

We study some properties of mean curvature flow solitons in general Riemannian manifolds and in warped products, with emphasis on constant curvature and Schwarzschild type spaces. We focus on splitting and rigidity results under various geometric conditions, ranging from the stability of the soliton to the fact that the image of its Gauss map be contained in suitable regions of the sphere. We also investigate the case of entire graphs

A splitting theorem for capillary graphs under Ricci lower bounds

In this paper, we study capillary graphs defined on a domain $\Omega$ of a complete Riemannian manifold $M$, where a graph is said to be capillary if it has constant mean curvature and locally constant Dirichlet and Neumann conditions on $\partial \Omega$. Our main result is a splitting theorem both for $\Omega$ and for the graph function on a class of manifolds with nonnegative Ricci curvature. As a corollary, we classify capillary graphs over domains that are globally Lipschitz epigraphs or slabs in a product space $M = N \times \mathbb{R}$, where $N$ has slow volume growth and non-negative Ricci curvature, including the case $M = \mathbb{R}^2,\mathbb{R}^3$. A technical core of the paper is a new gradient estimate for positive CMC graphs on manifolds with Ricci lower bounds.Comment: 42 pages. Bibliography updated. Accepted on J. Funct. Ana

On minimal graphs of sublinear growth over manifolds with non-negative Ricci curvature

We prove that entire solutions of the minimal hypersurface equation $$\mathrm{div}\left(\frac{Du}{\sqrt{1+|Du|^2}}\right) = 0$$ on a complete manifold with $\mathrm{Ric} \ge 0$, whose negative part grows like $\mathcal{O}(r/\log r)$ ($r$ the distance from a fixed origin), are constant. This extends the Bernstein Theorem for entire positive minimal graphs established in recent years. The proof depends on a new technique to get gradient bounds by means of integral estimates, which does not require any further geometric assumption on $M$.Comment: 19 pages. Comments are welcome

Joint Radar Target Detection and Parameter Estimation with MIMO OTFS

Motivated by future automotive applications, we study the joint target detection and parameter estimation problem using orthogonal time frequency space (OTFS), a digital modulation format robust to time-frequency selective channels. Assuming the transmitter is equipped with a mono-static MIMO radar, we propose an efficient maximum likelihood based approach to detect targets and estimate the corresponding delay, Doppler, and angle-of-arrival parameters. In order to reduce the computational complexity associated to the high-dimensional search, our scheme proceeds in two steps, i.e., target detection and coarse parameter estimation followed by refined parameter estimation. Interestingly, our numerical results demonstrate that the proposed scheme is able to identify multiple targets if they are separated in at least one domain out of three (delay, Doppler, and angle), while achieving the Cram\'er-Rao lower bound for the parameter estimation

Beam-Space MIMO Radar for Joint Communication and Sensing with OTFS Modulation

Motivated by automotive applications, we consider joint radar sensing and data communication for a system operating at millimeter wave (mmWave) frequency bands, where a Base Station (BS) is equipped with a co-located radar receiver and sends data using the Orthogonal Time Frequency Space (OTFS) modulation format. We consider two distinct modes of operation. In Discovery mode, a single common data stream is broadcast over a wide angular sector. The radar receiver must detect the presence of not yet acquired targets and perform coarse estimation of their parameters (angle of arrival, range, and velocity). In Tracking mode, the BS transmits multiple individual data streams to already acquired users via beamforming, while the radar receiver performs accurate estimation of the aforementioned parameters. Due to hardware complexity and power consumption constraints, we consider a hybrid digital-analog architecture where the number of RF chains and A/D converters is significantly smaller than the number of antenna array elements. In this case, a direct application of the conventional MIMO radar approach is not possible. Consequently, we advocate a beam-space approach where the vector observation at the radar receiver is obtained through a RF-domain beamforming matrix operating the dimensionality reduction from antennas to RF chains. Under this setup, we propose a likelihood function-based scheme to perform joint target detection and parameter estimation in Discovery, and high-resolution parameter estimation in Tracking mode, respectively. Our numerical results demonstrate that the proposed approach is able to reliably detect multiple targets while closely approaching the Cramer-Rao Lower Bound (CRLB) of the corresponding parameter estimation problem.Comment: 33 Page