Four lectures on scalar curvature
M Gromov - arXiv preprint arXiv:1908.10612, 2019 - arxiv.org
arXiv:1908.10612v6 [math.DG] 8 Jul 2021 Page 1 arXiv:1908.10612v6 [math.DG] 8 Jul 2021
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …
Conjectures on convergence and scalar curvature
C Sormani - arXiv preprint arXiv:2103.10093, 2021 - World Scientific
Here we survey the compactness and geometric stability conjectures formulated by the
participants at the 2018 IAS Emerging Topics Workshop on Scalar Curvature and …
participants at the 2018 IAS Emerging Topics Workshop on Scalar Curvature and …
dp–convergence and 𝜖–regularity theorems for entropy and scalar curvature lower bounds
MC Lee, A Naber, R Neumayer - Geometry & Topology, 2023 - msp.org
Consider a sequence of Riemannian manifolds (M in, gi) whose scalar curvatures and
entropies are bounded from below by small constants R i, μ i≥− 𝜖 i. The goal of this paper is …
entropies are bounded from below by small constants R i, μ i≥− 𝜖 i. The goal of this paper is …
Drawstrings and flexibility in the georch conjecture
D Kazaras, K Xu - arXiv preprint arXiv:2309.03756, 2023 - arxiv.org
In this paper, we observe new phenomena related to the structure of 3-manifolds satisfying
lower scalar curvature bounds. We construct warped-product manifolds of almost …
lower scalar curvature bounds. We construct warped-product manifolds of almost …
Almost non-negative scalar curvature on Riemannian manifolds conformal to tori
B Allen - The Journal of Geometric Analysis, 2021 - Springer
In this article we reduce the geometric stability conjecture for the scalar torus rigidity theorem
to the conformal case via the Yamabe problem. Then we are able to prove the case where a …
to the conformal case via the Yamabe problem. Then we are able to prove the case where a …
Ricci-Deturck flow from rough metrics and applications
J Chu, MC Lee - arXiv preprint arXiv:2204.05843, 2022 - arxiv.org
Motivated by the recent work of Lamm and Simon, in this work we study the short-time
existence theory of Ricci-Deturck flow starting from rough metrics which are bi-Lipschitz and …
existence theory of Ricci-Deturck flow starting from rough metrics which are bi-Lipschitz and …
Relating notions of convergence in geometric analysis
We relate L p convergence of metric tensors or volume convergence to a given smooth
metric to intrinsic flat and Gromov–Hausdorff convergence for sequences of Riemannian …
metric to intrinsic flat and Gromov–Hausdorff convergence for sequences of Riemannian …
Stability of the positive mass theorem and torus rigidity theorems under integral curvature bounds
B Allen, E Bryden, D Kazaras - arXiv preprint arXiv:2210.04340, 2022 - arxiv.org
Work of D. Stern and Bray-Kazaras-Khuri-Stern provide differential-geometric identities
which relate the scalar curvature of Riemannian 3-manifolds to global invariants in terms of …
which relate the scalar curvature of Riemannian 3-manifolds to global invariants in terms of …
Volume above distance below
Given a pair of metric tensors $ g_1\ge g_0 $ on a Riemannian manifold, $ M $, it is well
known that $\operatorname {Vol} _1 (M)\ge\operatorname {Vol} _0 (M) $. Furthermore one …
known that $\operatorname {Vol} _1 (M)\ge\operatorname {Vol} _0 (M) $. Furthermore one …
Stability of graphical tori with almost nonnegative scalar curvature
Abstract By works of Schoen–Yau and Gromov–Lawson any Riemannian manifold with
nonnegative scalar curvature and diffeomorphic to a torus is isometric to a flat torus. Gromov …
nonnegative scalar curvature and diffeomorphic to a torus is isometric to a flat torus. Gromov …