Károly J. Böröczky, Alessio Figalli, João P. G. Ramos
We prove that if a triplet of functions satisfies almost equality in the Pr'ekopa-Leindler inequality, then these functions are close to a common log-concave function, up to multiplication and rescaling. Our result holds for general measurable functions in all dimensions, and provides a quantitative stability estimate with computable constants.
{"title":"A quantitative stability result for the Prékopa–Leindler inequality for arbitrary measurable functions","authors":"Károly J. Böröczky, Alessio Figalli, João P. G. Ramos","doi":"10.4171/aihpc/97","DOIUrl":"https://doi.org/10.4171/aihpc/97","url":null,"abstract":"We prove that if a triplet of functions satisfies almost equality in the Pr'ekopa-Leindler inequality, then these functions are close to a common log-concave function, up to multiplication and rescaling. Our result holds for general measurable functions in all dimensions, and provides a quantitative stability estimate with computable constants.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"49 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135366985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result for the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions in the case of a massive Klein-Gordon field and a massless Dirac field. The nonlinearities are below-critical in two spatial dimensions, and so our method requires the identification of special structures within the system and novel weighted energy estimates. Another key advance, is that our proof allows us to weaken certain conditions on the nonlinear structures that have been assumed in the literature.
{"title":"Asymptotic stability for the Dirac–Klein–Gordon system in two space dimensions","authors":"Shijie Dong, Zoe Wyatt","doi":"10.4171/aihpc/103","DOIUrl":"https://doi.org/10.4171/aihpc/103","url":null,"abstract":"We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result for the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions in the case of a massive Klein-Gordon field and a massless Dirac field. The nonlinearities are below-critical in two spatial dimensions, and so our method requires the identification of special structures within the system and novel weighted energy estimates. Another key advance, is that our proof allows us to weaken certain conditions on the nonlinear structures that have been assumed in the literature.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"21 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135413269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result for a twisted Hesse-Koszul flow on any compact Hessian manifold. These results give alternative proofs for the existence of the unique Hesse-Einstein metric by Cheng-Yau and Caffarelli-Viaclovsky as well as the real Calabi theorem by Cheng-Yau, Delanoe and Caffarelli-Viaclovsky.
{"title":"Convergence of the Hesse–Koszul flow on compact Hessian manifolds","authors":"Stéphane Puechmorel, Tat Dat Tô","doi":"10.4171/aihpc/68","DOIUrl":"https://doi.org/10.4171/aihpc/68","url":null,"abstract":"We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result for a twisted Hesse-Koszul flow on any compact Hessian manifold. These results give alternative proofs for the existence of the unique Hesse-Einstein metric by Cheng-Yau and Caffarelli-Viaclovsky as well as the real Calabi theorem by Cheng-Yau, Delanoe and Caffarelli-Viaclovsky.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136078198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Global weak solutions of the Serre–Green–Naghdi equations with surface tension","authors":"Billel Guelmame","doi":"10.4171/aihpc/99","DOIUrl":"https://doi.org/10.4171/aihpc/99","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134989483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Gradient flow for $beta$-symplectic critical surfaces","authors":"Xiaoli Han, Jiayu Li, Jun Sun","doi":"10.4171/aihpc/100","DOIUrl":"https://doi.org/10.4171/aihpc/100","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135740162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Blowup of two-dimensional attractive Bose–Einstein condensates at the critical rotational speed","authors":"Van Duong Dinh, Dinh-Thi Nguyen, N. Rougerie","doi":"10.4171/aihpc/94","DOIUrl":"https://doi.org/10.4171/aihpc/94","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"29 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77926347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dispersive estimates for the Schrödinger equation in a model convex domain and applications","authors":"Oana Ivanovici","doi":"10.4171/aihpc/75","DOIUrl":"https://doi.org/10.4171/aihpc/75","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"74 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77016898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given compact Riemannian manifolds $mathcal{M}$ and $mathcal{N}$, a Riemannian covering $pi : smash{widetilde{mathcal{N}}} to mathcal{N}$ by a noncompact covering space $smash{widetilde{mathcal{N}}}$, $11$ and an optimal nonlinear fractional Sobolev estimate is obtained when moreover $sp ge dim mathcal{M}$. A nonlinear characterization of the sum of spaces $smash{dot{W}^{s, p}} (mathcal{M}, mathbb{R}) + smash{dot{W}^{1, sp}} (mathcal{M}, mathbb{R})$ is also provided.
给定紧致黎曼流形 $mathcal{M}$ 和 $mathcal{N}$黎曼覆盖 $pi : smash{widetilde{mathcal{N}}} to mathcal{N}$ 通过一个非紧的覆盖空间 $smash{widetilde{mathcal{N}}}$， $11$ 得到最优非线性分数Sobolev估计 $sp ge dim mathcal{M}$． 空间和的非线性表征 $smash{dot{W}^{s, p}} (mathcal{M}, mathbb{R}) + smash{dot{W}^{1, sp}} (mathcal{M}, mathbb{R})$ 也提供了。
{"title":"Lifting of fractional Sobolev mappings to noncompact covering spaces","authors":"Jean Van Schaftingen","doi":"10.4171/aihpc/98","DOIUrl":"https://doi.org/10.4171/aihpc/98","url":null,"abstract":"Given compact Riemannian manifolds $mathcal{M}$ and $mathcal{N}$, a Riemannian covering $pi : smash{widetilde{mathcal{N}}} to mathcal{N}$ by a noncompact covering space $smash{widetilde{mathcal{N}}}$, $1<p<infty$ and $0<s<1$, the space of liftings of fractional Sobolev maps in $smash{dot{W}^{s, p}} (mathcal{M}, mathcal{N})$ is characterized when $sp>1$ and an optimal nonlinear fractional Sobolev estimate is obtained when moreover $sp ge dim mathcal{M}$. A nonlinear characterization of the sum of spaces $smash{dot{W}^{s, p}} (mathcal{M}, mathbb{R}) + smash{dot{W}^{1, sp}} (mathcal{M}, mathbb{R})$ is also provided.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"81 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89158885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the sharp scattering threshold for the mass–energy double critical nonlinear Schrödinger equation via double track profile decomposition","authors":"Yongming Luo","doi":"10.4171/aihpc/71","DOIUrl":"https://doi.org/10.4171/aihpc/71","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"30 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84266069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On symmetric div-quasiconvex hulls and divsym-free $L^infty$-truncations","authors":"Linus Behn, F. Gmeineder, Stefanie Schiffer","doi":"10.4171/aihpc/66","DOIUrl":"https://doi.org/10.4171/aihpc/66","url":null,"abstract":"","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"10 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82232267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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