Weighted isoperimetric inequalities and some applications
加权等周不等式和一些应用
基本信息
- 批准号:2525697
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:英国
- 项目类别:Studentship
- 财政年份:2021
- 资助国家:英国
- 起止时间:2021 至 无数据
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
The classical isoperimetric inequality is a relation between the perimeter and volume of a set in Euclidean space. Balls minimise perimeter uniquely amongst competitor sets with the same volume. This geometric inequality entails a number of analytic inequalities. In particular it entails the Pólya-Szegö inequality under Steiner or Schwarz symmetrisation. This can be used in turn to obtain the best constant in the Sobolev inequality. An application is the Rayleigh-Faber-Krahn inequality which says that the ball has smallest Dirichlet ground state eigenvalue amongst domains with the same volume. This is a basic result in the fields of Spectral Geometry and Shape Optimisation.In recent years attention has focused on what happens when both perimeter and volume are measured with respect to a density. The volume and perimeter densities may be the same or different.Existence and boundedness results for the isoperimetric problem with density are contained in [Morgan and Pratelli (2013)] and [De Philippis, Franzina, Pratelli (2015)]. An analogue of the first-mentioned result is contained in [McGillivray (2021)] in the planar case with radial perimeter and volume weights. An aim is to obtain an analogue of the second-mentioned result in the two-weighted situation when the density with respect to the metric converges from below (in the radial case in the first instance).The log-concave density conjecture has been proved in [Chambers (2015)] and states (roughly) that centred balls in Euclidean space are isoperimetric minimisers if the density is log-convex. A version with weaker hypotheses in the planar case is contained in [McGillivray (2018)]. A counterpart on the hyperbolic plane is contained in [McGillivray (2019)]. An aim is to explore whether there is also some counterpart on the punctured sphere. The log-convex density conjecture arose out of stability considerations. It is hoped that a similar approach might yield a corresponding conjecture for the punctured sphere. A particular case in the two-weighted situation is when the volume and perimeter weights are radial powers. For certain exponents centred balls are uniquely isoperimetric. We refer to [Alvino, Brock, Chiacchio, Mercaldo and Posteraro (2017)]. This last was extended in [McGillivray (2021)] proving a conjecture contained there and in [Diaz, Harman, Howe, Thompson (2012)]. A corresponding Pólya-Szegö inequality is obtained in the paper of Alvino et al as well as a Caffarelli-Kohn-Nirenberg inequality (a counterpart of the Sobolev inequality with weights). An aim is to obtain analogues of these analytic inequalities in the case covered in [McGillivray (2021)].
经典的等周不等式是欧几里德空间中一个集合的周长和体积之间的关系。在相同体积的比赛中,球的周长是独一无二的。这个几何不等式包含了许多解析不等式。特别地,它需要在施泰纳或施瓦茨对称下的Pólya-Szegö不等式。这可以用来得到Sobolev不等式的最佳常数。一个应用是Rayleigh-Faber-Krahn不等式,它说球在相同体积的域中具有最小的狄利克雷基态特征值。这是光谱几何和形状优化领域的基本结果。近年来,人们的注意力集中在测量周长和体积相对于密度时会发生什么。体积密度和周长密度可能相同,也可能不同。具有密度的等周问题的存在性和有界性结果包含在[Morgan and Pratelli(2013)]和[De Philippis, Franzina, Pratelli(2015)]中。在具有径向周长和体积权重的平面情况下,[McGillivray(2021)]中包含了第一个提到的结果的模拟。目的是在密度相对于度规从下面收敛(在第一个实例的径向情况下)的双加权情况下获得第二个提到的结果的模拟。log-凹密度猜想已经在[Chambers(2015)]中得到证明,并且(粗略地)表明,如果密度是log-凸的,欧几里得空间中的中心球是等周最小的。在平面情况下具有较弱假设的版本包含在[McGillivray(2018)]中。双曲平面上的对应项包含在[McGillivray(2019)]中。目的是探索是否在被击穿的球体上也有一些对应物。对数凸密度猜想是出于稳定性考虑而产生的。我们希望类似的方法可以对穿孔球产生相应的猜想。在双加权情况下的一个特殊情况是体积和周长的权重是径向幂。对于某些指数,中心球是唯一等周的。我们参考[Alvino, Brock, Chiacchio, Mercaldo and Posteraro(2017)]。后者在[McGillivray(2021)]中得到扩展,证明了其中和[Diaz, Harman, Howe, Thompson(2012)]中包含的一个猜想。在Alvino等人的论文中得到了一个相应的Pólya-Szegö不等式以及一个Caffarelli-Kohn-Nirenberg不等式(带权的Sobolev不等式的对应)。目的是在[McGillivray(2021)]所涵盖的情况下获得这些解析不等式的类似物。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
其他文献
吉治仁志 他: "トランスジェニックマウスによるTIMP-1の線維化促進機序"最新医学. 55. 1781-1787 (2000)
Hitoshi Yoshiji 等:“转基因小鼠中 TIMP-1 的促纤维化机制”现代医学 55. 1781-1787 (2000)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
LiDAR Implementations for Autonomous Vehicle Applications
- DOI:
- 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
吉治仁志 他: "イラスト医学&サイエンスシリーズ血管の分子医学"羊土社(渋谷正史編). 125 (2000)
Hitoshi Yoshiji 等人:“血管医学与科学系列分子医学图解”Yodosha(涉谷正志编辑)125(2000)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Effect of manidipine hydrochloride,a calcium antagonist,on isoproterenol-induced left ventricular hypertrophy: "Yoshiyama,M.,Takeuchi,K.,Kim,S.,Hanatani,A.,Omura,T.,Toda,I.,Akioka,K.,Teragaki,M.,Iwao,H.and Yoshikawa,J." Jpn Circ J. 62(1). 47-52 (1998)
钙拮抗剂盐酸马尼地平对异丙肾上腺素引起的左心室肥厚的影响:“Yoshiyama,M.,Takeuchi,K.,Kim,S.,Hanatani,A.,Omura,T.,Toda,I.,Akioka,
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('', 18)}}的其他基金
An implantable biosensor microsystem for real-time measurement of circulating biomarkers
用于实时测量循环生物标志物的植入式生物传感器微系统
- 批准号:
2901954 - 财政年份:2028
- 资助金额:
-- - 项目类别:
Studentship
Exploiting the polysaccharide breakdown capacity of the human gut microbiome to develop environmentally sustainable dishwashing solutions
利用人类肠道微生物群的多糖分解能力来开发环境可持续的洗碗解决方案
- 批准号:
2896097 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
A Robot that Swims Through Granular Materials
可以在颗粒材料中游动的机器人
- 批准号:
2780268 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Likelihood and impact of severe space weather events on the resilience of nuclear power and safeguards monitoring.
严重空间天气事件对核电和保障监督的恢复力的可能性和影响。
- 批准号:
2908918 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Proton, alpha and gamma irradiation assisted stress corrosion cracking: understanding the fuel-stainless steel interface
质子、α 和 γ 辐照辅助应力腐蚀开裂:了解燃料-不锈钢界面
- 批准号:
2908693 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Field Assisted Sintering of Nuclear Fuel Simulants
核燃料模拟物的现场辅助烧结
- 批准号:
2908917 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Assessment of new fatigue capable titanium alloys for aerospace applications
评估用于航空航天应用的新型抗疲劳钛合金
- 批准号:
2879438 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Developing a 3D printed skin model using a Dextran - Collagen hydrogel to analyse the cellular and epigenetic effects of interleukin-17 inhibitors in
使用右旋糖酐-胶原蛋白水凝胶开发 3D 打印皮肤模型,以分析白细胞介素 17 抑制剂的细胞和表观遗传效应
- 批准号:
2890513 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Understanding the interplay between the gut microbiome, behavior and urbanisation in wild birds
了解野生鸟类肠道微生物组、行为和城市化之间的相互作用
- 批准号:
2876993 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
相似海外基金
CAREER: Geometric Aspects of Isoperimetric and Sobolev-type Inequalities
职业:等周和索博列夫型不等式的几何方面
- 批准号:
2340195 - 财政年份:2024
- 资助金额:
-- - 项目类别:
Continuing Grant
Higher rank hyperbolicity and homological isoperimetric inequalities
高阶双曲性和同调等周不等式
- 批准号:
2896389 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Studentship
Higher rank hyperbolicity and homological isoperimetric inequalities
高阶双曲性和同调等周不等式
- 批准号:
2785744 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Studentship
Isometric embeddings, isoperimetric inequalities and geometric nonlinear PDE
等距嵌入、等周不等式和几何非线性 PDE
- 批准号:
RGPIN-2018-04443 - 财政年份:2022
- 资助金额:
-- - 项目类别:
Discovery Grants Program - Individual
Erdos-Ko-Rado type problems, Isoperimetric inequalities, and other topics in Combinatorics.
Erdos-Ko-Rado 类型问题、等周不等式以及组合学中的其他主题。
- 批准号:
2614845 - 财政年份:2021
- 资助金额:
-- - 项目类别:
Studentship
Erdos-Ko-Rado type problems, Isoperimetric inequalities, and other topics in Combinatorics.
Erdos-Ko-Rado 类型问题、等周不等式以及组合学中的其他主题。
- 批准号:
2611263 - 财政年份:2021
- 资助金额:
-- - 项目类别:
Studentship
Isometric embeddings, isoperimetric inequalities and geometric nonlinear PDE
等距嵌入、等周不等式和几何非线性 PDE
- 批准号:
RGPIN-2018-04443 - 财政年份:2021
- 资助金额:
-- - 项目类别:
Discovery Grants Program - Individual
Isometric embeddings, isoperimetric inequalities and geometric nonlinear PDE
等距嵌入、等周不等式和几何非线性 PDE
- 批准号:
RGPIN-2018-04443 - 财政年份:2020
- 资助金额:
-- - 项目类别:
Discovery Grants Program - Individual
Isometric embeddings, isoperimetric inequalities and geometric nonlinear PDE
等距嵌入、等周不等式和几何非线性 PDE
- 批准号:
RGPIN-2018-04443 - 财政年份:2019
- 资助金额:
-- - 项目类别:
Discovery Grants Program - Individual
Isometric embeddings, isoperimetric inequalities and geometric nonlinear PDE
等距嵌入、等周不等式和几何非线性 PDE
- 批准号:
RGPIN-2018-04443 - 财政年份:2018
- 资助金额:
-- - 项目类别:
Discovery Grants Program - Individual