• 대한수학회보
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• 제59권6호
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• pp.1423-1438
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• 2022

In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.

• 한국수학교육학회지시리즈A:수학교육
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• 제32권2호
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• pp.173-177
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• 1993

• 대한수학회지
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• 제56권2호
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• pp.421-437
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• 2019

We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.

• 대한수학회지
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• 제39권5호
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• pp.731-743
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• 2002

Let M be a Riemannian manifold with asymptotically non-negative curvature. We study the asymptotic behavior of the energy densities of a harmonic map and an exponentially harmonic function on M. We prove that the energy density of a bounded harmonic map vanishes at infinity when the target is a Cartan-Hadamard manifold. Also we prove that the energy density of a bounded exponentially harmonic function vanishes at infinity.