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of 45
pro vyhledávání: '"De Ponti, Nicolò"'
For the Laplacian of an $n$-Riemannian manifold $X$, the Weyl law states that the $k$-th eigenvalue is asymptotically proportional to $(k/V)^{2/n}$, where $V$ is the volume of $X$. We show that this result can be derived via physical considerations b
Externí odkaz:
http://arxiv.org/abs/2406.00095
Autor:
De Ponti, Nicolò, Stefani, Giorgio
We prove several functional and geometric inequalities only assuming the linearity and a quantitative $\mathrm{L}^\infty$-to-Lipschitz smoothing of the heat semigroup in metric-measure spaces. Our results comprise a Buser inequality, a lower bound on
Externí odkaz:
http://arxiv.org/abs/2403.00620
We obtain a vanishing result for solutions of the inequality $|\Delta u|\le q_1|u|+q_2|\nabla u|$ that decay to zero along a very general warped cylindrical end of a Riemannian manifold. The appropriate decay condition at infinity on $u$ is related t
Externí odkaz:
http://arxiv.org/abs/2401.12367
We prove the Pleijel theorem in non-collapsed RCD spaces, providing an asymptotic upper bound on the number of nodal domains of Laplacian eigenfunctions. As a consequence, we obtain that the Courant nodal domain theorem holds except at most for a fin
Externí odkaz:
http://arxiv.org/abs/2307.13983
Publikováno v:
J. High Energ. Phys. 2023, 127 (2023)
In models with extra dimensions, matter particles can be easily localized to a 'brane world', but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to
Externí odkaz:
http://arxiv.org/abs/2306.05456
Publikováno v:
SciPost Phys. 15, 039 (2023)
We prove an equivalence between the classical equations of motion governing vacuum gravity compactifications (and more general warped-product spacetimes) and a concavity property of entropy under time evolution. This is obtained by linking the theory
Externí odkaz:
http://arxiv.org/abs/2212.02511
Publikováno v:
Transactions of the American Mathematical Society, Series B. 9/13/202024, Vol. 11, p1138-1182. 45p.
Publikováno v:
J. High Energ. Phys. 2021, 217 (2021)
We consider gravity compactifications whose internal space consists of small bridges connecting larger manifolds, possibly noncompact. We prove that, under rather general assumptions, this leads to a massive spin-two field with very small mass. The a
Externí odkaz:
http://arxiv.org/abs/2109.11560
Autor:
De Ponti, Nicolò, Farinelli, Sara
In the paper we prove two inequalities in the setting of ${\sf RCD}(K,\infty)$ spaces using similar techniques. The first one is an indeterminacy estimate involving the $p$-Wasserstein distance between the positive part and the negative part of an $L
Externí odkaz:
http://arxiv.org/abs/2104.12097
Autor:
De Ponti, Nicoló, Mondino, Andrea
Publikováno v:
Probab. Theory Related Fields 184 (2022), no. 1-2, 159--208
Inspired by the recent theory of Entropy-Transport problems and by the $\mathbf{D}$-distance of Sturm on normalised metric measure spaces, we define a new class of complete and separable distances between metric measure spaces of possibly different t
Externí odkaz:
http://arxiv.org/abs/2009.10636