Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Aaron Naber"'
Publikováno v:
Geometry & Topology. 27:227-350
Publikováno v:
Perspectives in Scalar Curvature ISBN: 9789811249983
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::19b6e33a70ae4a0c7649abe75c01040f
https://doi.org/10.1142/9789811273223_0003
https://doi.org/10.1142/9789811273223_0003
Autor:
Nan Li, Aaron Naber
Publikováno v:
Peking Mathematical Journal. 3:203-234
Let $X\in\text{Alex}\,^n(-1)$ be an $n$-dimensional Alexandrov space with curvature $\ge -1$. Let the $r$-scale $(k,\epsilon)$-singular set $\mathcal S^k_{\epsilon,\,r}(X)$ be the collection of $x\in X$ so that $B_r(x)$ is not $\epsilon r$-close to a
Autor:
Daniele Valtorta, Aaron Naber
Publikováno v:
Journal of the European Mathematical Society. 22:3305-3382
If one considers an integral varifold Im ⊆ M with bounded mean curvature, and if Sk(I) ≡ {x ∈ M : no tangent cone at x is k + 1-symmetric} is the standard stratification of the singular set, then it is well known that dim Sk(I) ≤ k. In comple
Publikováno v:
Annals of Mathematics. 193
Autor:
Wenshuai Jiang, Aaron Naber
Publikováno v:
Annals of Mathematics. 193
Consider a Riemannian manifold with bounded Ricci curvature $|\Ric|\leq n-1$ and the noncollapsing lower volume bound $\Vol(B_1(p))>\rv>0$. The first main result of this paper is to prove that we have the $L^2$ curvature bound $\fint_{B_1(p)}|\Rm|^2
Autor:
Aaron Naber
In this short note we review some known results on the structure and regularity of spaces with lower Ricci curvature bounds. We present some known and new open questions about next steps.
v2: Corollary 2.20 corrected
v2: Corollary 2.20 corrected
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d0fb6575da7dd1b85bde10739d26f67a
http://arxiv.org/abs/2010.10031
http://arxiv.org/abs/2010.10031
Recall that if $(M^n,g)$ satisfies $\mathrm{Ric}\geq 0$, then the Li-Yau Differential Harnack Inequality tells us for each nonnegative $f:M\to \mathbb{R}^+$, with $f_t$ its heat flow, that $\frac{\Delta f_t}{f_t}-\frac{|\nabla f_t|^2}{f_t^2} +\frac{n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a1ac54b60da3bded8df0d34549d6176
Autor:
Aaron Naber, Robert Haslhofer
Publikováno v:
Journal of the European Mathematical Society. 20:1269-1302
Autor:
Daniele Valtorta, Aaron Naber
Publikováno v:
Communications on Pure and Applied Mathematics. 70:1835-1897
In this paper we study solutions to elliptic linear equations $L(u)=\partial_i(a^{ij}(x)\partial_j u) + b^i(x) \partial_i u + c(x) u=0$, either on $R^n$ or a Riemannian manifold, under the assumption of Lipschitz control on the coefficients $a^{ij}$.