Hong-Wei ZHANG

    Institut Denis Poisson
    Université d'Orléans
    Bâtiment de Mathématiques
    45067 Orléans cedex 2

    hong-wei.zhang at sign

     Curriculum Vitae

Research Interests 

Harmonic analysis and PDE on Riemannian symmetric and locally symmetric spaces of non-compact type

Research Papers


[5] Thesis: équation des ondes sur les espaces symétriques et localement symétriques de type non compact, (.pdf), (.slides)

By adding a detailed introduction (in French), this thesis collects the research papers [1]-[4]

Wave equation on general noncompact symmetric spaces, with J.-Ph. Anker, preprint, (.pdf)

Wave equation on certain noncompact symmetric spaces, preprint, (.pdf)

The wave equation on symmetric spaces has been considered for many years, see for instance Semenov-Tian-Shansky, Helgason, Branson, etc.. The interesting feature about non-compact symmetric spaces is their rapid growth at infinity. This means that properties of PDE such as dispersion are more pronounced. This phenomenon has been progressively understood on real hyperbolic spaces since 2000, see for example Ionescu, Tataru, Metcalfe&Taylor, Anker&Pierfelice, etc., and these results can be extended without difficulty to all non-compact symmetric spaces of rank one. In these two papers, the wave equation is studied in general rank. After considering  various special symmetric spaces in [3], we give in [4] the definitive solution to the problem on general symmetric space of non-compact type. This is achieved by overcoming a well-known difficulty in higher rank analysis, namely the fact that the Plancherel density is not a differential symbol in general. We establish the time-sharp pointwise kernel estimates and the dispersion properties for the wave equation. As consequence, we deduce the global-in-time Strichartz inequality for a large family of admissible pairs and prove global well-posedness results for the corresponding semilinear equation with low regularity data.


Bottom of the L2 spectrum of the Laplacian on locally symmetric spaces, with J.-Ph. Anker, preprint, (.pdf)

In this paper, we estimate the bottom of the L2 spectrum of the Laplacian on locally symmetric spaces in terms of the critical exponents of appropriate Poincaré series. Our main result is the higher rank analog of a characterization due to Elstrodt, Patterson, Sullivan and Corlette in rank one. It improves upon previous results obtained by Leuzinger and Weber in higher rank.

[1] Wave and Klein-Gordon equations on certain locally symmetric spaces, J. Geom. Anal. 30 (2020), no. 4, 4386-4406, (.pdf)

This paper is devoted to study the dispersion properties of the linear Klein-Gordon and wave equations on a class of locally symmetric spaces. We extend the previous results obtained on non-compact symmetric spaces of rank one to more general locally symmetric spaces, which are convex cocompact and satisfy that the half sum of positive roots is greater than the critical exponent of the Poincaré series. This setting has been also considered in Burq&Guillarmou&Hassell and Fotiadis&Mandouvalos&Marias for studying the Schrödinger equation.

Hong-Wei ZHANG –

Jan. 2020: Wave equation on certain symmetric spaces. (.slides)

Introduction to spherical Fourier analysis on noncompact symmetric spaces. (.slides)

Workshop: Harmonic Analysis and Applications, TSIMF, Sanya, China

Dec. 2018: Wave and Klein-Gordon equations on certain locally symmetric spaces. (.slides) 

  Conference: The Legacy of Joseph Fourier after 250 years, TSIMF, Sanya, China

Nov. 2018: Équations des ondes sur certains espaces localement symétriques. (.slides)

Seminar: Journée des doctorants, Orléans, France

*Last updated: 15/12/2020