Ước lượng giá trị riêng của toán tử Laplace thông qua số lượng tập con giảm thiểu

Springer Science and Business Media LLC - Tập 217 - Trang 413-433 - 2017
Kei Funano1
1Division of Mathematics & Research Center for Pure and Applied Mathematics Graduate School of Information Sciences, Tohoku University, Sendai, Japan

Tóm tắt

Bất đẳng thức Chung–Grigor’yan–Yau mô tả các giới hạn trên của giá trị riêng của toán tử Laplace dưới dạng các tập con (“đầu vào”) và thể tích của chúng. Trong bài báo này, chúng tôi sẽ chứng minh rằng có thể giảm thiểu “đầu vào” trong bất đẳng thức Chung–Grigor’yan–Yau trong bối cảnh các không gian Alexandrov thỏa mãn CD(0,∞). Chúng tôi cũng sẽ thảo luận về một giả thuyết liên quan cho một bất đẳng thức phổ quát giữa các giá trị riêng của toán tử Laplace.

Từ khóa

#bất đẳng thức Chung–Grigor’yan–Yau #giá trị riêng #toán tử Laplace #không gian Alexandrov #giả thuyết

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