Annali di Matematica Pura ed Applicata最新文献

Singular Riemannian foliations, variational problems and principles of symmetric criticalities 奇异黎曼叶，变分问题和对称临界原理

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-05-26 DOI: 10.1007/s10231-026-01679-z

Marcos M. Alexandrino, Leonardo F. Cavenaghi, Diego Corro, Marcelo K. Inagaki

{"title":"Singular Riemannian foliations, variational problems and principles of symmetric criticalities","authors":"Marcos M. Alexandrino, Leonardo F. Cavenaghi, Diego Corro, Marcelo K. Inagaki","doi":"10.1007/s10231-026-01679-z","DOIUrl":"10.1007/s10231-026-01679-z","url":null,"abstract":"<div>A singular foliation (mathscr {F}) on a complete Riemannian manifold M is called a Singular Riemannian foliation (SRF for short) if its leaves are locally equidistant, e.g., the partition of M into the orbits of a Lie group action by isometries. In this paper, we investigate variational problems in compact Riemannian manifolds equipped with SRFs with special properties, which we name as AVP. Examples of such SRFs being considered include isoparametric foliations, SRFs on Euclidean fiber bundles, and the partition of M into the orbits of a Lie group acting by isometries. More precisely, we prove an analog to Palais’ Principle of Symmetric Criticality for (mathscr {F})-symmetric integral operators on the Banach spaces (W^{1,p}(M).) This result together with a version of the Rellich–Kondrachov–Hebey–Vaugon Embedding Theorem for (mathscr {F})-basic Sobolev functions allows us to circumvent difficulties with Sobolev’s critical exponents when considering applications of techniques from Calculus of Variations to find solutions to PDEs. To exemplify this, we prove the existence of countably infinite many weak solutions to a class of variational problems, which includes p-Kirchhoff problems for manifolds equipped with an AVP foliation.</div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 5","pages":"2507 - 2572"},"PeriodicalIF":0.9,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01679-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Elliptic Weingarten surfaces of minimal type invariant by left translations in (textrm{Sol}_3) 中的最小型不变椭圆Weingarten曲面的左平移 (textrm{Sol}_3)

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-05-12 DOI: 10.1007/s10231-026-01674-4

Albetã C. Mafra, Carlos Peñafiel, Erick J. Palacios Escobar

引用次数: 0

Total (mathbb {A})-variation flows 总(mathbb {A}) -变化流量

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-05-06 DOI: 10.1007/s10231-026-01688-y

David Meyer

引用次数: 0

Reduction principles for proper actions 适当行动的还原原则

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-04-26 DOI: 10.1007/s10231-026-01687-z

Leonardo Biliotti, Gustavo May-Custodio, Alessandro Minuzzo

{"title":"Reduction principles for proper actions","authors":"Leonardo Biliotti, Gustavo May-Custodio, Alessandro Minuzzo","doi":"10.1007/s10231-026-01687-z","DOIUrl":"10.1007/s10231-026-01687-z","url":null,"abstract":"<div>\u0000 \u0000 We study the core of a proper action by a Lie group G on a smooth manifold M, extending the construction for G compact by Skjelbred and Straume (A note on the reduction principle for compact transformation groups, 1995). Moreover, we show that many properties of a proper G-action on M are determined by the action of a group (G') on the corresponding core ( _cM). We say that such properties admit a reduction principle. In particular, we prove that a proper isometric G-action on M is polar (resp. hyperpolar) if and only if the (G')-action on ( _cM) is polar (resp. hyperpolar). In the case of a proper action by symplectomorphisms on a symplectic manifold, we show that a reduction principle holds for coisotropic and infinitesimally almost homogeneous actions. We further study the coisotropic condition for the case of a proper Hamiltonian action and its relation with the symplectic stratification described by Lermann and Bates (Pac J Math 181:201–229, 1997). In particular, we obtain several characterizations for coisotropic actions, some of which extend known results for the action of a compact group of holomorphic automorphisms on a compact Kähler manifold obtained by Huckleberry and Wurzbacher (Math Ann 286:261–280, 1990). Finally, we study some applications of the core construction for the action of a compact Lie group on a Kähler manifold by holomorphic isometries.\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 5","pages":"2777 - 2817"},"PeriodicalIF":0.9,"publicationDate":"2026-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01687-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Groups of order 64 and non-homeomorphic double Kodaira fibrations with the same biregular invariants 具有相同双正则不变量的64阶群和非同胚双Kodaira纤颤

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-04-17 DOI: 10.1007/s10231-026-01691-3

Francesco Polizzi, Pietro Sabatino

引用次数: 0

Energy asymptotics and blow-up phenomena for biharmonic Brézis-Nirenberg problem 双调和brsamzis - nirenberg问题的能量渐近性和爆破现象

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-04-17 DOI: 10.1007/s10231-026-01684-2

Jiamo Li, Qikai Lu, Minbo Yang

{"title":"Energy asymptotics and blow-up phenomena for biharmonic Brézis-Nirenberg problem","authors":"Jiamo Li, Qikai Lu, Minbo Yang","doi":"10.1007/s10231-026-01684-2","DOIUrl":"10.1007/s10231-026-01684-2","url":null,"abstract":"<div>\u0000 \u0000 For dimensions (nge 8), we are concerned with the quotient functional of the biharmonic Brézis-Nirenberg problem under the Navier boundary condition <div><div>$$ S(varepsilon V):=inf _{0not equiv uin H^2(Omega )cap H_0^1(Omega )}frac{int _{Omega }|Delta u|^2dx+varepsilon int _{Omega }V|u|^2dx}{big (int _{Omega }|u|^{2^star }dxbig )^{2/2^star }}, $$</div></div>where (2^star =frac{2n}{n-4}) is the critical Sobolev exponent of the embedding (H^2(Omega )cap H_0^1(Omega )hookrightarrow L^{2^star }(Omega )), (Omega subset mathbb {R}^n) is a bounded open set and (V:overline{Omega }rightarrow mathbb {R}) is a continuous function. Under certain assumptions on V, we establish sharp asymptotics for the energy difference (S(0)-S(varepsilon V)), as (varepsilon rightarrow 0^+), by means of matching upper and lower bound estimates. Moreover, we give a precise description of the blow-up profile of (almost) minimizing sequences and characterize the blow-up rate and the location of concentration points.\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 5","pages":"2679 - 2704"},"PeriodicalIF":0.9,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A uniqueness result in the inverse problem for the anisotropic Schrödinger type equation from local measurements 从局部测量得到各向异性Schrödinger型方程反问题的唯一性结果

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-04-17 DOI: 10.1007/s10231-026-01686-0

Niall Donlon, Romina Gaburro

引用次数: 0

Remark on Laplacians and Riemannian submersions with totally geodesic fibers 全测地线纤维的拉普拉斯和黎曼浸没

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-04-17 DOI: 10.1007/s10231-026-01682-4

Kazumasa Narita

{"title":"Remark on Laplacians and Riemannian submersions with totally geodesic fibers","authors":"Kazumasa Narita","doi":"10.1007/s10231-026-01682-4","DOIUrl":"10.1007/s10231-026-01682-4","url":null,"abstract":"<div>\u0000 \u0000 Given a Riemannian submersion ((M,g) rightarrow (B,j)) each of whose fibers is connected and totally geodesic, we consider a certain 1-parameter family of Riemannian metrics ((g_{t})_{t > 0}) on M, which is called the canonical variation. Let (lambda _{1}(g_{t})) be the first positive eigenvalue of the Laplace–Beltrami operator (Delta ^{M}_{g_{t}}) and (hbox {Vol}(M,g_{t})) the volume of ((M, g_{t})). In Bérard-Bergery and Bourguignon (Ill J Math 26(2):181–200,1982 ) showed that the scale-invariant quantity (lambda _{1}(g_{t})hbox {Vol}(M,g_{t})^{2/hbox {dim}M}) goes to 0 with t. In this paper, we show that if each fiber is Einstein and (M, g) satisfies a certain condition about its Ricci curvature, then bounds for (lambda _{1}(g_{t})) can be obtained. In particular this implies that (lambda _{1}(g_{t})hbox {Vol}(M,g_{t})^{2/hbox {dim}M}) goes to (infty ) with t. Moreover, using these bounds, we consider stability of (g_{t}) as a critical point of the Yamabe functional.\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 5","pages":"2629 - 2650"},"PeriodicalIF":0.9,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the blow up of (C^1) solutions of the isentropic Euler system 等熵欧拉系统(C^1)解的爆破

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-04-17 DOI: 10.1007/s10231-026-01680-6

Shyam Sundar Ghoshal, Animesh Jana

{"title":"On the blow up of (C^1) solutions of the isentropic Euler system","authors":"Shyam Sundar Ghoshal, Animesh Jana","doi":"10.1007/s10231-026-01680-6","DOIUrl":"10.1007/s10231-026-01680-6","url":null,"abstract":"<div>In this article, we study the break-down of smooth and continuous solutions to isentropic Euler system in multi dimension. Sideris (Comm Math Phys 101(4):475–478, 1985) proved the blow up of smooth solutions when initial data satisfies an ‘integral condition’. We show that a (C^1) solution of isentropic Euler equation breaks down if (i) gradient of initial velocity has a negative real eigenvalue at some point (x_0in mathbb {R}^d) and (ii) Hessian of initial density satisfies a smallness condition in Sobolev space. Our proof also works for the data which fails to satisfy the above-mentioned ‘integral condition’. Furthermore, we prove the global existence of smooth solution when (i) eigenvalues of gradient of initial velocity have non-negative real-part and (ii) initial density satisfies a smallness condition. This extends the global existence result of Grassin (Indiana Univ Math J 47(4):1397–1432, 1998). Another goal of this article is to study the breakdown of continuous weak solutions of isentropic Euler equations. We are able to show that the ‘integral condition’ of Sideris can cause the breakdown of continuous solutions in finite time. This improves the blow up result of Sideris from (C^1) to continuous space.</div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 5","pages":"2573 - 2609"},"PeriodicalIF":0.9,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fujita exponent for heat equation with Hörmander vector fields 具有Hörmander向量场的热方程的Fujita指数

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-04-17 DOI: 10.1007/s10231-026-01683-3

Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky

引用次数: 0