# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## The gaps in the spectrum of the Schrödinger operator

### Tom 69 / 2005

Banach Center Publications 69 (2005), 91-102 MSC: Primary 35P15; Secondary 58G25. DOI: 10.4064/bc69-0-5

#### Streszczenie

We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain $\Omega$ of a submanifold $M$ in $R^{N}$ with boundary $\partial \Omega$, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau's result.

#### Autorzy

• Haizhong LiDepartment of Mathematical Sciences
Tsinghua University
Beijing, 100084
People's Republic of China
e-mail
• Linlin SuDepartment of Mathematical Sciences
Tsinghua University
Beijing, 100084
People's Republic of China

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