in which h is the
second fundamental form of the boundary of M, H is its
mean curvature, and ν is its unit normal vector.[2][3] This is often used in combination with the observation
with the consequence that
This is particularly useful since one can now make use of the solvability of the Dirichlet problem for the Laplacian to make useful choices for u.[4][5] Applications include eigenvalue estimates in
spectral geometry and the study of submanifolds of
constant mean curvature.
Bennett Chow, Peng Lu, and Lei Ni. Hamilton's Ricci flow. Graduate Studies in Mathematics, 77. American Mathematical Society, Providence, RI; Science Press Beijing, New York, 2006. xxxvi+608 pp.
ISBN978-0-8218-4231-7,
0-8218-4231-5
Tobias Holck Colding and William P. Minicozzi II. A course in minimal surfaces. Graduate Studies in Mathematics, 121. American Mathematical Society, Providence, RI, 2011. xii+313 pp.
ISBN978-0-8218-5323-8.
doi:
10.1090/gsm/121
R. Schoen and S.-T. Yau. Lectures on differential geometry. Lecture notes prepared by Wei Yue Ding, Kung Ching Chang, Jia Qing Zhong and Yi Chao Xu. Translated from the Chinese by Ding and S.Y. Cheng. With a preface translated from the Chinese by Kaising Tso. Conference Proceedings and Lecture Notes in Geometry and Topology, I. International Press, Cambridge, MA, 1994. v+235 pp.
ISBN1-57146-012-8
in which h is the
second fundamental form of the boundary of M, H is its
mean curvature, and ν is its unit normal vector.[2][3] This is often used in combination with the observation
with the consequence that
This is particularly useful since one can now make use of the solvability of the Dirichlet problem for the Laplacian to make useful choices for u.[4][5] Applications include eigenvalue estimates in
spectral geometry and the study of submanifolds of
constant mean curvature.
Bennett Chow, Peng Lu, and Lei Ni. Hamilton's Ricci flow. Graduate Studies in Mathematics, 77. American Mathematical Society, Providence, RI; Science Press Beijing, New York, 2006. xxxvi+608 pp.
ISBN978-0-8218-4231-7,
0-8218-4231-5
Tobias Holck Colding and William P. Minicozzi II. A course in minimal surfaces. Graduate Studies in Mathematics, 121. American Mathematical Society, Providence, RI, 2011. xii+313 pp.
ISBN978-0-8218-5323-8.
doi:
10.1090/gsm/121
R. Schoen and S.-T. Yau. Lectures on differential geometry. Lecture notes prepared by Wei Yue Ding, Kung Ching Chang, Jia Qing Zhong and Yi Chao Xu. Translated from the Chinese by Ding and S.Y. Cheng. With a preface translated from the Chinese by Kaising Tso. Conference Proceedings and Lecture Notes in Geometry and Topology, I. International Press, Cambridge, MA, 1994. v+235 pp.
ISBN1-57146-012-8