Explanipedia

Cannabidiol as a Prophylactic Agent Against Glioblastoma Growth: A Preclinical Investigation Open

Lei P. Wang, Bidhan Bhandari, Sahar Emami Naeini, Benjamin D. Hill, Hannah M. Rogers , et al. · 2025

Purpose: Glioblastoma (GBM) is one of the most aggressive brain tumors, with limited treatment options and poor outcomes due to frequent relapse after surgery. This study aims to investigate whether pretreatment with inhaled cannabidiol (C…

Boosting Acetylcholine Signaling by Cannabidiol in a Murine Model of Alzheimer’s Disease Open

Hesam Khodadadi, Évila Lopes Salles, Sahar Emami Naeini, Bidhan Bhandari, Hannah M. Rogers , et al. · 2024

Alzheimer’s disease (AD) is a challenging medical issue that requires efficacious treatment options to improve long-term quality of life. Cannabidiol (CBD) is a cannabis-derived phytocannabinoid with potential health benefits, including re…

Table of Contents Open

Christopher Pellegrino, Kevin Koo, Amanda North, Gina M. Badalato, Gopal Badlani , et al. · 2024

Geometry of branched minimal surfaces of finite index Open

William H. Meeks, Joaquín Pérez · 2024

Given I , B ∈ N ∪ { 0 } $I,B\in \mathbb{N}\cup \left\{0\right\}$ , we investigate the existence and geometry of complete finitely branched minimal surfaces M in R 3 ${\mathbb{R}}^{3}$ with Morse index at most I and total bran…

Geometry of constant mean curvature surfaces in $\mathbb{R}^{3}$ Open

William H. Meeks, Giuseppe Tinaglia · 2024

The crowning achievement of this paper is the proof that round spheres are the only complete, simply-connected surfaces embedded in \mathbb{R}^{3} with nonzero constant mean curvature. Fundamental to this proof are new results including th…

Hierarchy structures in finite index CMC surfaces Open

William H. Meeks, Joaquín Pérez · 2023

Given ε 0 > 0 {{\varepsilon}_{0}>0} , I ∈ ℕ ∪ { 0 } {I\in\mathbb{N}\cup\{0\}} and K 0 , H 0 ≥ 0 {K_{0},H_{0}\geq 0} , let X be a complete Riemannian 3-manifold with injectivity radius Inj ⁡ ( X ) ≥ ε 0 {\o…

Modifications preserving hyperbolicity of link complements Open

Colin Adams, William H. Meeks, Álvaro Ramos · 2023

Given a link in a 3-manifold such that the complement is hyperbolic, we provide two modifications to the link, called the chain move and the switch move, that preserve hyperbolicity of the complement, with only a relatively small number of…

Table of Contents Open

Vahid Mehrnoush, Fatemeh Darsareh, Ahmed Kotb, Ahmed S. Zakaria, Hazem Elmansy , et al. · 2023

Geometry of CMC surfaces of finite index Open

William H. Meeks, Joaquín Pérez · 2023

Given r 0 > 0 {r}_{0}\gt 0 , I ∈ N ∪ { 0 } I\in {\mathbb{N}}\cup \left\{0\right\} , and K 0 , H 0 ≥ 0 {K}_{0},{H}_{0}\ge 0 , let X X be a complete Riemannian 3-manifold with injectivity radius Inj ( X ) …

Sexual Dimorphism in the Polarization of Cardiac ILCs through Elabela Open

Évila Lopes Salles, Sahar Emami Naeini, Bidhan Bhandari, Hesam Khodadadi, Edie Threlkeld , et al. · 2022

Elabela is a component of the apelinergic system and may exert a cardioprotective role by regulating the innate immune responses. Innate lymphoid cells (ILCs) have a significant role in initiating and progressing immune-inflammatory respon…

Geometry of CMC surfaces of finite index Open

William H. Meeks, Joaquín Pérez · 2022

Given $r_0>0$, $I\in \mathbb{N}\cup \{0\}$ and $K_0,H_0\geq 0$, let $X$ be a complete Riemannian $3$-manifold with injectivity radius $\mbox{Inj}(X)\geq r_0$ and with the supremum of absolute sectional curvature at most $K_0$, and let $M\l…

Hierarchy structures in finite index CMC surfaces Open

William H. Meeks, Joaquín Pérez · 2022

Given $\varepsilon_0>0$, $I\in \mathbb{N}\cup \{0\}$ and $K_0,H_0\geq0$, let $X$ be a complete Riemannian $3$-manifold with injectivity radius $\mbox{Inj}(X)\geq \varepsilon_0$ and with the supremum of absolute sectional curvature at most …

Geometry of branched minimal surfaces of finite index Open

William H. Meeks, Joaquín Pérez · 2022

Given $I,B\in\mathbb{N}\cup \{0\}$, we investigate the existence and geometry of complete finitely branched minimal surfaces $M$ in $\mathbb{R}^3$ with Morse index at most $I$ and total branching order at most $B$. Previous works of Fische…

Congenitally absent left atrial appendage: cardiac CTA and TEE correlation Open

William H. Meeks, Ryan Wilson, David C. Isbell · 2022

A woman in her late 70s with a medical history of paroxysmal atrial fibrillation which failed cardioversion and pharmacological rhythm control was referred to electrophysiology for consideration of ablation. A cardiac CTA was performed bas…

The embedded Calabi–Yau conjecture for finite genus Open

William H. Meeks, Joaquín Pérez, Antonio R�os · 2021

Suppose $M$ is a complete, embedded minimal surface in $\mathbb{R}^3$ with an infinite number of ends, finite genus and compact boundary. We prove that the simple limit ends of $M$ have properly embedded representatives with compact bounda…

A nonexistence result for CMC surfaces in hyperbolic 3-manifolds Open

William H. Meeks, Álvaro Ramos · 2021

We prove that a complete hyperbolic 3-manifold of finite volume does not admit a properly embedded noncompact surface of finite topology with constant mean curvature greater than or equal to 1.

Limit lamination theorem for H-disks Open

William H. Meeks, Giuseppe Tinaglia · 2021

Constant mean curvature spheres in homogeneous three-manifolds Open

William H. Meeks, Pablo Mira, Joaquín Pérez, Antonio R�os · 2020

Totally umbilic surfaces in hyperbolic 3-manifolds of finite volume Open

Colin Adams, William H. Meeks, Álvaro Ramos · 2020

We construct for every connected surface $S$ of finite negative Euler characteristic and every $H \in [0,1)$, a hyperbolic 3-manifold $N(S,H)$ of finite volume and a proper, two-sided, totally umbilic embedding $f\colon S\to N(S,H)$ with m…

Modifications Preserving Hyperbolicity of Link Complements Open

Colin Adams, William H. Meeks, Álvaro Ramos · 2020

Given a link in a 3-manifold such that the complement is hyperbolic, we provide two modifications to the link, called the chain move and the switch move, that preserve hyperbolicity of the complement, with only a relatively small number of…

One-sided curvature estimates for H-disks Open

William H. Meeks, Giuseppe Tinaglia · 2020

In this paper we prove an extrinsic one-sided curvature estimate for disks embedded in $\mathbb{R}^3$ with constant mean curvature which is independent of the value of the constant mean curvature. We apply this extrinsic one-sided curvatur…

Curvature estimates for constant mean curvature surfaces Open

William H. Meeks, Giuseppe Tinaglia · 2019

We derive extrinsic curvature estimates for compact disks embedded in $\\mathbb{R}^{3}$ with nonzero constant mean curvature.

Properly immersed surfaces in hyperbolic $3$-manifolds Open

William H. Meeks, Álvaro Ramos · 2019

We study complete finite topology immersed surfaces $Σ$ in complete Riemannian $3$-manifolds $N$ with sectional curvature $K_N\leq -a^2\leq 0$, such that the absolute mean curvature function of $Σ$ is bounded from above by $a$ and its inje…

Limit Lamination Theorems for H-surfaces Open

William H. Meeks, Giuseppe Tinaglia · 2019

In this paper we prove some general results for constant mean curvature lamination limits of certain sequences of compact surfaces M _n embedded in ℝ ³ with constant mean curvature H _n and fixed finite genus…

Structure theorems for singular minimal laminations Open

William H. Meeks, Joaquín Pérez, Antonio R�os · 2019

We apply the local removable singularity theorem for minimal laminations [W. H. Meeks III, J. Pérez and A. Ros, Local removable singularity theorems for minimal laminations, J. Differential Geom. 103 (2016), no. 2, 319–362] and the local p…

Bounds on the topology and index of minimal surfaces Open

William H. Meeks, Joaquín Pérez, Antonio R�os · 2019

We prove that for every nonnegative integer $g$, there exists a bound on the number of ends of a complete, embedded minimal surface $M$ in $\mathbb{R}^3$ of genus $g$ and finite topology. This bound on the finite number of ends when $M$ ha…

Triply periodic constant mean curvature surfaces Open

William H. Meeks, Giuseppe Tinaglia · 2018

Given a closed flat 3-torus N, for each H > 0 and each nonnegative integer g, we obtain area estimates for closed surfaces with genus g and constant mean curvature H embedded in N. This result contrasts with the theorem of Traizet [31], wh…

Triply periodic constant mean curvature surfaces Open

William H. Meeks, Giuseppe Tinaglia · 2018

The local picture theorem on the scale of topology Open

William H. Meeks, Joaquín Pérez, Antonio R�os · 2018

We prove a descriptive theorem on the extrinsic geometry of an embedded minimal surface of injectivity radius zero in a homogeneously regular Riemannian three-manifold, in a certain small intrinsic neighborhood of a point of almost-minimal…

The geometry of stable minimal surfaces in metric Lie groups Open

William H. Meeks, Pablo Mira, Joaquín Pérez · 2018

We study geometric properties of compact stable minimal surfaces with boundary in homogeneous 3-manifolds $X$ that can be expressed as a semidirect product of $\mathbb {R}^2$ with $\mathbb {R}$ endowed with a left invariant metric. For any…

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