partially supported by the ANR,programme blanc GEOMETRYA ANR-12-BS01-0014;the European Community Marie Curie grant MANET 607643 and H2020 grant GHAIA 777822;the Simons Collaborations in MPS grant 601941,GD;supported by the NSF INSPIRE Award DMS1344235;NSF CAREER Award DMS 1220089;the NSF RAISE-TAQ grant DMS 1839077;the Simons Fellowship;the Simons Foundation grant 563916,SM
The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of n-1 dimensional sets across analysis, geometric measure theory, and PDEs. The p...
The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit.Local active coordinate sys...
Supported by NSFC(Grant Nos.11171091,11371018);partially supported by NSF of He'nan Province(Grant No.132300410141)
In this paper,we obtain a sufficient and necessary condition for a simply connected Riemannian manifold(M^n,g) to be isometrically immersed,as a submanifold with codimension p 〉 1,into the product S^k×H^n+p+k of...
We determine a 2-codimensional para-CR structure on the slit tangent bundle T0 M of a Finsler manifold(M,F) by imposing a condition regarding the almost paracomplex structure P associated to F when restricted to the...
This work gives a classification theorem for affine immersions with planar geodesics in the case where the codimension is maximal. Vrancken classified parallel affine immersions in this case and obtained, among others...
This work was conducted in part during October 15-22, 2000 at the Stefan Banach International Mathematical Center at Warsaw and June 24-26, 2001 at the Mathematical Center at Bedlewo, supported by"Research in groups"grants
Let f, g : X→Y be two maps between closed manifolds with dim X ≥ dim Y = n ≥ 3. We study the primary obstruction on(f, g) to deforming f and g to be coincidence free on the n-th skeleton of X. We give examples f...