## 656 Citations

### A P ] 11 S ep 2 01 3 Logarithmically-concave moment measures

- Mathematics
- 2014

We discuss a certain Riemannian metric, related to the toric Kähler-Einstein equation, that is associated in a linearly-invariant manner with a giv en log-concave measure in Rn. We use this metric in…

### Eigenvalue Estimates for $p$-Laplace Problems on Domains Expressed in Fermi Coordinates

- Mathematics
- 2021

We prove explicit and sharp eigenvalue estimates for Neumann p-Laplace eigenvalues in domains that admit a representation in Fermi coordinates. More precisely, if γ denotes a non-closed curve in R…

### Functional Inequalities on Weighted Riemannian Manifolds Subject to Curvature-Dimension Conditions

- Mathematics
- 2019

We establish new sharp inequalities of Poincare or log-Sobolev type, on geodesically-convex weighted Riemannian manifolds $(M,\mathfrak{g},\mu)$ whose (generalized) Ricci curvature…

### Sharp Poincaré inequalities in a class of non-convex sets

- MathematicsJournal of Spectral Theory
- 2018

Let $\gamma$ be a smooth curve whose image is symmetric with respect to the y-axis, and let D be a planar domain consisting of the points on one side of $\gamma$, within a suitable distance $\delta$…

### Stabilization to trajectories and approximate controllability for the equations of fluid mechanics / eingereicht von Duy Phan-Duc

- Mathematics
- 2016

This dissertation is devoted to three main problems: Gevrey regularity, approximate controllability and stabilization to trajectories for some equations of fluid mechanics. The Gevrey regularity…

### On Constants in Maxwell Inequalities for Bounded and Convex Domains

- Mathematics
- 2015

It is shown that for a bounded and convex domain Ω ⊂ ℝ3, the Maxwell constants are bounded from below and above by the Friedrichs and Poincaré constants of Ω, respectively. Bibliography: 14 titles.

### Needle decompositions in Riemannian geometry

- Mathematics
- 2014

The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, our method is based on the following…

### Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator

- Mathematics
- 2012

The purpose of this manuscript is to present a series of lecture notes on isoperimetric inequalities for the Laplacian, for the Schrödinger operator, and related problems.

### A Proof of Bobkov's Spectral Bound For Convex Domains via Gaussian Fitting and Free Energy Estimation

- Mathematics
- 2012

We obtain a new proof of Bobkov's lower bound on the first positive eigenvalue of the (negative) Neumann Laplacian (or equivalently, the Cheeger constant) on a bounded convex domain $K$ in Euclidean…

### An optimal Poincare inequality in L^1 for convex domains

- Mathematics
- 2003

For convex domains Ω C R n with diameter d we prove ∥u∥ L 1 (ω) ≤ d 2 ∥⊇ u ∥ L 1 (ω) for any u with zero mean value on w. We also show that the constant 1/2 in this inequality is optimal.

## References

SHOWING 1-7 OF 7 REFERENCES

### Methoden der mathematischen Physik

- Philosophy
- 1924

VIII uber den Inhalt im einzelnen unterrichtet das ausfuhrliche Ver zeichnis. Zur Form ist etwas Grundsatzliches zu sagen: Das klassische Ideal einer gewissermassen atomistischen Auffassung der…

### Lower Bounds for Vibration Frequencies of Elastically Supported Membranes and Plates

- Mathematics
- 1957

If R is two-dimensional, the eigenvalues Xi(k) are proportional to the squares of the frequencies of a membrane covering R and elastically supported on the boundary B. If R is three-dimensional they…

### New bounds for solutions of second order elliptic partial differential equations

- Mathematics
- 1958

1. Introduction In a previous paper [10] the authors presented methods for determining, with arbitrary and known accuracy, the Dirichlet integral and the value at a point of a solution of Laplace's…