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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The logarithmic Brunn-Minkowski inequality conjecture in convex geometry
凸几何 对数 布伦-闵可夫斯基 不等式猜想
2023/4/21
The logarithmic Brunn-Minkowski inequality conjecture is one of the most intriguing challenges in convex geometry since 2012. Notably, this conjectured inequality is stronger than the celebrated Brunn...
HARNACK INEQUALITY AND HYPERBOLICITY FOR SUBELLIPTIC p-LAPLACIANS WITH APPLICATIONS TO PICARD TYPE THEOREMS
HARNACK INEQUALITY HYPERBOLICITY
2015/8/26
Let M be a complete non-compact Riemannian manifold. For p ∈ (1,+∞),
let Δp be the p-Laplace operator on M. One says that M is p-hyperbolic
if there exists a Green function for Δp (see [Ho1,2]); oth...
A quantitative isoperimetric inequality for fractional perimeters
quantitative isoperimetric inequality fractional perimeters
2011/1/14
Recently Frank & Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here ...
A curved Brunn--Minkowski inequality on the discrete hypercube
A curved Brunn--Minkowski inequality discrete hypercube
2010/11/24
We compare two approaches to Ricci curvature on non-smooth spaces, in the case of the discrete hypercube $\{0,1\}^N$. While the coarse Ricci curvature of the first author readily yields a positive va...
The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients
The Harnack inequality related properties elliptic
2010/11/15
We discuss the problem how "bad" may be lower-order coefficients in elliptic and parabolic second order equations to ensure some qualitative properties of solution such as strong maximum principle, H...
A Simple Proof of the Geometric-Arithmetic Mean Inequality
Arithmetic mean Geometric mean Inequality
2010/1/25
In this short note, we give another proof of the Geometric-Arithmetic Mean inequality.
The Refinement and Reverse of a Geometric Inequality
Geometric inequality Best constant Triangle
2010/4/16
In this paper, we give a refinement and a reverse of a geometric inequality in a triangle posed by Jiang [2] by making use of the equivalent form of a fundamental inequality [6] and classic analysis.
An Inequality on Ternary Quadratic Forms in Triangles
Positive semidefinite ternary quadratic form arithmetic-mean geometric-mean inequality Cauchy inequality triangle
2010/1/22
In this short note, we give a proof of a conjecture about ternary quadratic orms involving two triangles and several interesting applications.
An Elementary Proof of Blundon's Inequality
Blundon's Inequality Geometric Inequality Arithmetic-Geometric Mean Inequality
2010/1/22
In this note, we give an elementary proof of Blundon's Inequality. We make use of a simple auxiliary result, provable by only using the Arithmetic Mean - Geometric Mean Inequality.
An Extension of the Erdös-Debrunner Inequality to General Power Means
Erdö s-Debrunner inequality harmonic mean geometric mean power means
2010/1/22
Given the harmonic mean of the numbers () and a , we determine the best power mean exponents and such that , where and only depend on . Also, for we similarly handle the estimates.
Petty Projection Inequality for $L_p$-Mixed Projection Body
petty projection inequality $L_p$-projection body $L_p$-mixed projection body $L_p$-centroid body $L_p$-mixed quermassintegrals
2007/12/12
Recently, Lutwak, Yang and Zhang posed the notion of $L_p$-projection body and established the $L_p$-analog of the Petty projection inequality. In this paper, the notion of $L_p$-mixed projection body...
Inequality for Ricci Curvature of Slant Submanifolds in Cosymplectic Space Forms
Mean curvature sectional curvature k-Ricci curvature slant submanifold semi-slant submanifold bi-slant submanifold cosymplectic space form
2010/2/26
In this article, we establish inequalities between the Ricci curvature and the squared mean curvature, and also between the k-Ricci curvature and the scalar curvature for a slant, semi-slant and bi-sl...
The Inequality of Moser and Trudinger and appli ations to onformal geometry
The Inequality of Moser Trudinger appli ations onformal geometry
2014/4/3
The Inequality of Moser and Trudinger and appli ations to onformal geometry。
Let $p(z)$ be a monic polynomial of degree $n$, with complex coefficients, and let $q(z)$ be its monic factor. We prove an asymptotically sharp inequality of the form $\|q\|_{E} \le C^n \|p\|_E$, whe...