A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications
In this paper, we derive a Reilly type formula for the diffusion-type operator $\mathcal{L}\cdot=\frac{1}{B}\textrm{div}(A\nabla\cdot)$ on weighted manifolds with boundary, where $A$ and $B$ are two positive smooth functions on manifolds. As its applications, some inequalities of Poincaré type, Cole...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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oai:jmag.ilt.kharkiv.ua:article-10712024-12-10T20:10:43Z A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications Zeng, Fanqi Chang, Huiting Sun, Yujun формула типу Рейлi оператор дифузiйного типу m-модифiкована кривина Рiччi A-середня кривина Reilly type formula diffusion-type operator m-modified Ricci curvature A-mean curvature In this paper, we derive a Reilly type formula for the diffusion-type operator $\mathcal{L}\cdot=\frac{1}{B}\textrm{div}(A\nabla\cdot)$ on weighted manifolds with boundary, where $A$ and $B$ are two positive smooth functions on manifolds. As its applications, some inequalities of Poincaré type, Colesanti type, Minkowski type and Heintze-Karcher type are provided. Mathematical Subject Classification 2020: 53C21, 58J32 У цій статті ми виводимо формулу типу Рейлі для оператора дифузійного типу $\mathcal{L}\cdot=\frac{1}{B}\textrm{div}(A\nabla\cdot)$ на зважених многовидах із межею, де $A$ і $B$ - дві додатні гладкі функції на многовидах. В якості її застосування наведено деякі нерівності типу Пуанкаре, Колесанті, Мінковського та Хайнце-Карчера. Mathematical Subject Classification 2020: 53C21, 58J32 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2024-06-29 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1071 10.15407/mag20.02.250 Journal of Mathematical Physics, Analysis, Geometry; Vol. 20 No. 2 (2024); 250–264 Журнал математической физики, анализа, геометрии; Том 20 № 2 (2024); 250–264 Журнал математичної фізики, аналізу, геометрії; Том 20 № 2 (2024); 250–264 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1071/jm20-0250e |
| institution |
Journal of Mathematical Physics, Analysis, Geometry |
| baseUrl_str |
|
| datestamp_date |
2024-12-10T20:10:43Z |
| collection |
OJS |
| language |
English |
| topic |
формула типу Рейлi оператор дифузiйного типу m-модифiкована кривина Рiччi A-середня кривина |
| spellingShingle |
формула типу Рейлi оператор дифузiйного типу m-модифiкована кривина Рiччi A-середня кривина Zeng, Fanqi Chang, Huiting Sun, Yujun A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications |
| topic_facet |
формула типу Рейлi оператор дифузiйного типу m-модифiкована кривина Рiччi A-середня кривина Reilly type formula diffusion-type operator m-modified Ricci curvature A-mean curvature |
| format |
Article |
| author |
Zeng, Fanqi Chang, Huiting Sun, Yujun |
| author_facet |
Zeng, Fanqi Chang, Huiting Sun, Yujun |
| author_sort |
Zeng, Fanqi |
| title |
A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications |
| title_short |
A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications |
| title_full |
A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications |
| title_fullStr |
A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications |
| title_full_unstemmed |
A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications |
| title_sort |
reilly type integral formula associated with diffusion-type operators and its applications |
| title_alt |
A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications A Reilly Type Integral Formula Associated with Diffusion-Type Operators and Its Applications |
| description |
In this paper, we derive a Reilly type formula for the diffusion-type operator $\mathcal{L}\cdot=\frac{1}{B}\textrm{div}(A\nabla\cdot)$ on weighted manifolds with boundary, where $A$ and $B$ are two positive smooth functions on manifolds. As its applications, some inequalities of Poincaré type, Colesanti type, Minkowski type and Heintze-Karcher type are provided.
Mathematical Subject Classification 2020: 53C21, 58J32 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2024 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1071 |
| work_keys_str_mv |
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2025-09-26T01:40:44Z |
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2025-09-26T01:40:44Z |
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