A remark on Schottky representations and Reidemeister torsion

The present paper establishes a formula of Reidemeister torsion for Schottky representations. The theoretical results are applied to 3-manifolds with boundary consisting orientable surfaces with genus at least 2

A remark on elliptic differential equations on manifold

For elliptic boundary value problems of nonlocal type in Euclidean space, the well posedness has been studied by several authors and it has been well understood. On the other hand, such kind of problems on manifolds have not been studied yet. Present article considers differential equations on smooth closed manifolds. It establishes the well posedness of nonlocal boundary value problems of elliptic type, namely Neumann-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds and also DirichletBitsadze-Samarskii type nonlocal boundary value problem on manifolds, in H¨older spaces. In addition, in various H¨older norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifolds

A Note on Representation Variety of Abelian Groups and Reidemeister Torsion

4th International Conference on Analysis and Applied Mathematics, ICAAM 2018 -- 6 September 2018 through 9 September 2018 -- -- 262329Let S and G denote respectively the 2 - torus and one of the Lie groups GL (n, C), SL (n, C), SO (n, C), Sp (2 n, C). In the present article, we consider the smooth part of the representation variety Rep (S, G) consisting of conjugacy classes of homomorphisms from fundamental group ?1(S) to G. We show the well definiteness of Reidemeister torsion for such representations. In addition, we establish a formula for computing the Reidemeister torsion of such representations in terms of the symplectic structure on Rep (S, G) [51]. This symplectic form is analogous to Atiyah–Bott–Goldman symplectic form of higher genera for the Lie group G. © 2021, Springer Nature Switzerland AG.2-s2.0-8511219594

On bitsadze-samarskii type elliptic differential problems on hyperbolic plane

In the present article, we consider nonlocal boundary value problems (NBVP) of elliptic type on relatively compact domains in the hyperbolic plane. We establish the wellposedness of Neumann-Bitsadze-Samarskii type and also Dirichlet-Bitsadze-Samarskii type on such domains. Furthermore, we establish new coercivity inequalities for solutions of such elliptic NBVP on relatively compact domains in the hyperbolic plane with various H¨older norms. © 20212-s2.0-8510663313

A remark on elliptic differential equations on manifold

5th International Conference on Analysis and Applied Mathematics (ICAAM) -- SEP 23-30, 2020 -- Mersin, TURKEYFor elliptic boundary value problems of nonlocal type in Euclidean space, the well posedness has been studied by several authors and it has been well understood. On the other hand, such kind of problems on manifolds have not been studied yet. Present article considers differential equations on smooth closed manifolds. It establishes the well posedness of nonlocal boundary value problems of elliptic type, namely Neumann-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds and also Dirichlet-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds, in Holder spaces. In addition, in various Holder norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifolds.Near E UnivRUDN University Program 5-100The publication has been prepared with the support of the RUDN University Program 5-100WOS:00058059100000

A remark on elliptic differential equations on manifold

For elliptic boundary value problems of nonlocal type in Euclidean space, the well posedness has been studied by several authors and it has been well understood. On the other hand, such kind of problems on manifolds have not been studied yet. Present article considers differential equations on smooth closed manifolds. It establishes the well posedness of nonlocal boundary value problems of elliptic type, namely Neumann-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds and also Dirichlet-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds, in H¨older spaces. In addition, in various H¨older norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifoldsДля эллиптических краевых задач нелокального типа в евклидовом пространстве корректность поставленной задачи была хорошо изучена несколькими авторами. С другой стороны, такие проблемы на многообразиях широко не изучены. В настоящей статье рассмотрены дифференциальные уравнения на гладких замкнутых многообразиях. Установлена корректность нелокальных краевых задач эллиптического типа, а именно нелокальной краевой задачи типа Неймана-Бицадзе-Самарского на многообразиях, а также нелокальной краевой задачи типа Дирихле - Бицадзе - Самарского на многообразиях в пространствах Гольдера. Кроме того, в различных нормах Гольдера установлены новые неравенства коэрцитивности для решений краевых задач эллиптического нелокального типа на гладких многообразия

A remark on elliptic differential equations on manifold

For elliptic boundary value problems of nonlocal type in Euclidean space, the well posedness has been studied by several authors and it has been well understood. On the other hand, such kind of problems on manifolds have not been studied yet. Present article considers differential equations on smooth closed manifolds. It establishes the well posedness of nonlocal boundary value problems of elliptic type, namely Neumann-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds and also Dirichlet-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds, in Holder spaces. In addition, in various Holder norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifolds

A note on parabolic differential equations on manifold

The present extended abstract considers the differential equations on smooth closed manifolds, investigates and establishes the well-posedness of nonlocal boundary value problems (NBVP) in Hölder spaces. It also establishes new coercivity estimates in various Hölder norms for the solutions of such boundary value problems for parabolic equations. © 2021 American Institute of Physics Inc.. All rights reserved

A note on hyperbolic differential equations on manifold

In this extended abstract, considering the differential equations on hyperbolic plane, we investigate and establish the well-posedness of boundary value problem for hyperbolic equations in Hölder spaces. Furthermore, we establish new coercivity estimates in various Hölder norms for the solutions of such boundary value problems for hyperbolic equations. © 2021 Author(s)

On bitsadze-samarskii type elliptic differential problems on hyperbolic plane

In the present article, we consider nonlocal boundary value problems (NBVP) of elliptic type on relatively compact domains in the hyperbolic plane. We establish the wellposedness of Neumann-Bitsadze-Samarskii type and also Dirichlet-Bitsadze-Samarskii type on such domains. Furthermore, we establish new coercivity inequalities for solutions of such elliptic NBVP on relatively compact domains in the hyperbolic plane with various H¨older norms. © 202