| [1] | Alencar H, Colares A G. Integral formulas for the $r$-mean curvature linearized operator of a hypersurface. Ann Global Anal Geom, 1998, 16(3): 203-220 |
| [2] | Chen B, Yano K. Integral formulas for submanifolds and their applications. Journal of Differential Geometry, 1971, 5(3/4): 467-477 |
| [3] | Fraser A, Schoen R. The first Steklov eigenvalue, conformal geometry, and minimal surfaces. Advances in Mathematics, 2011, 226(5): 4011-4030 |
| [4] | Fraser A, Schoen R. Sharp eigenvalue bounds and minimal surfaces in the ball. Inventiones Mathematicae, 2016, 203(3): 823-890 |
| [5] | Garding L. An inequality for hyperbolic polynomials. Journal of Mathematics and Mechanics, 1959: 957-965 |
| [6] | Hsiung C C. Some integral formulas for closed hypersurfaces in Riemannian space. Pacific J Math, 1956, 6(2): 291-299 |
| [7] | Huisken G, Sinestrari C. Convexity estimates for mean curvature flow and singularities of mean convex surfaces. Acta Mathematica, 1999, 183(1): 45-70 |
| [8] | Koh S E. A characterization of round spheres. Proceedings of the American Mathematical Society, 1998, 126(12): 3657-3660 |
| [9] | Kwong K K. An extension of Hsiung-Minkowski formulas and some applications. The Journal of Geometric Analysis, 2016, 26(1): 1-23 |
| [10] | Li H, Xiong C. Stability of capillary hypersurfaces in a Euclidean ball. Pacific Journal of Mathematics, 2018, 297(1): 131-146 |
| [11] | Montiel S, Ros A. Compact hypersurfaces: The Alexandrov theorem for higher order mean curvatures. Differential Geometry, 1991, 52: 279-296 |
| [12] | Reilly R C. Variational properties of functions of the mean curvatures for hypersurfaces in space forms. Journal of Differential Geometry, 1973, 8(3): 465-477 |
| [13] | Ros A, Souam R. On stability of capillary surfaces in a ball. Pacific Journal of Mathematics, 1997, 178(2): 345-361 |
| [14] | Scheuer J, Wang G, Xia C. Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball. Journal of Differential Geometry, 2022, 120(2): 345-373 |
| [15] | Strübing W. On integral formulas for submanifolds of spaces of constant curvature and some applications. Manuscripta Mathematica, 1984, 49(2): 177-194 |
| [16] | Wang G, Weng L. A mean curvature type flow with capillary boundary in a unit ball. Calculus of Variations and Partial Differential Equations, 2020, 59: Article number 149 |
| [17] | Wang G, Xia C. Uniqueness of stable capillary hypersurfaces in a ball. Mathematische Annalen, 2019, 374(3): 1845-1882 |
| [18] | Wang G, Xia C. Guan-Li type mean curvature flow for free boundary hypersurfaces in a ball. arXiv: 1910.07253 |
| [19] | Wu J. A new characterization of geodesic spheres in the hyperbolic space. Proceedings of the American Mathematical Society, 2016, 144(7): 3077-3084 |
),Wang Yinhang*(