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L2 HARMONIC FORMS ON GRADIENT SHRINKING RICCI SOLITONS
윤갑진 대한수학회 2017 대한수학회지 Vol.54 No.4
In this paper, we study vanishing properties for $L^2$ harmonic $1$-forms on a gradient shrinking Ricci soliton. We prove that if $(M, g, f)$ is a complete oriented noncompact gradient shrinking Ricci soliton with potential function $f$, then there are no non-trivial $L^2$ harmonic $1$-forms which are orthogonal to $df$. Second, we show that if the scalar curvature of the metric $g$ is greater than or equal to $(n-2)/2$, then there are no non-trivial $L^2$ harmonic $1$-forms on $(M, g)$. We also show that any multiplication of the total differential $df$ by a function cannot be an $L^2$ harmonic $1$-form unless it is trivial. Finally, we derive various integral properties involving the potential function $f$ and $L^2$ harmonic $1$-forms, and handle their applications.
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윤갑진 대한흉부심장혈관외과학회 1984 Journal of Chest Surgery (J Chest Surg) Vol.17 No.3
For the treatment of acute respiratory failure and emergency care of an urgent patient, tracheostomy in itself may have been a life saving procedure. But, tracheal stenosis gives serious clinical manifestation which can only be corrected by surgical intervention in many occasions. We experienced one case of tracheal stenosis following tracheostomy for assisted ventilation. Tracheogram showed a 4.0 cm segmental narrowing below the tracheostoma. Before reconstruction, we tried to T-tube cannulation, but the result was not satisfactory. So we resected the narrowed segment and tracheal reconstruction was performed with uneventful result.
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윤갑진 대한흉부심장혈관외과학회 1984 Journal of Chest Surgery (J Chest Surg) Vol.17 No.1
A clinical evaluation was performed on 76 cases of chest injury experienced at department of Chest Surgery, Capital Armed Forces General Hospital during the past 3 years period from January 1981 to August 1983. 1.The most common cause of the chest trauma was gun shot by which 26 cases were injured among 44 cases [57.9%] of penetrating injury. Remaining 32 cases [42.1%] were injured by non-penetrating blunt trauma. 2.Hemopneumothorax was observed in 60 cases [78.9%], those were caused by both penetrating [65%] and non-penetrating [35%] injuries. 3.Rib fracture was found in 58.7% of total cases and with rib fracture, clavicle fracture was combined at 19.6% and sternal fracture, at 8.7%. 4.Most common symptoms were chest pain and dyspnea, and most common signs were breath sound diminution and subcutaneous emphysema. 5.Common site of rib fracture was from 4th rib to 8th rib [69.4%]. 6.In 58 cases [76.3%], patients were treated with operation including open thoracotomy [25 cases]. 7.Overall mortality was 5.3%[4 cases] and causes of death were septic shock and respiratory failure.
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윤갑진 대한흉부심장혈관외과학회 1984 Journal of Chest Surgery (J Chest Surg) Vol.17 No.1
Left ventricular-Right atrial canal is a rare congenital heart disease. The vast majority of the cases reported in the literature are clinically diagnosed as atrial septal defect or ventricular septal defect. The method of choice in establishing the diagnosis of left ventricular-right atrlal canal is selective left ventriculography. Recently we experienced one case of left ventricular-right atrial canal which was diagnosed as ventricular septal defect preoperatively. The type of defect was tricuspid perforation of infravalvular type, and repaired with direct suture. Postoperative course was uneventful and discharged without complication.
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Horizontally homothetic harmonic morphisms and stability of totally geodesic submanifolds
윤갑진,최건돈 대한수학회 2008 대한수학회지 Vol.45 No.2
In this article, we study the relations of horizontally homothetic harmonic morphisms with the stability of totally geodesic submanifolds. Let p : (Mn, g) → (Nm, h) be a horizontally homothetic harmonic morphism from a Riemannian manifold into a Riemannian manifold of non-positive sectional curvature and let T be the tensor measuring minimality or totally geodesics of fibers of p. We prove that if T is parallel and the horizontal distribution is integrable, then for any totally geodesic submanifold P in N, the inverse set, p-1(P), is volume-stable in M. In case that P is a totally geodesic hypersurface, the condition on the curvature can be weakened to Ricci curvature. In this article, we study the relations of horizontally homothetic harmonic morphisms with the stability of totally geodesic submanifolds. Let p : (Mn, g) → (Nm, h) be a horizontally homothetic harmonic morphism from a Riemannian manifold into a Riemannian manifold of non-positive sectional curvature and let T be the tensor measuring minimality or totally geodesics of fibers of p. We prove that if T is parallel and the horizontal distribution is integrable, then for any totally geodesic submanifold P in N, the inverse set, p-1(P), is volume-stable in M. In case that P is a totally geodesic hypersurface, the condition on the curvature can be weakened to Ricci curvature.
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L<sup>2</sup> 조화미분형식과 극소초평면에의 응용
윤갑진 대한수학회 2002 대한수학회논문집 Vol.17 No.2
본 요약논문에서는 리만다양체에서 정의되는 L$^2$조화미분 형식의 성질과 존재성에 대하여 알아보고 그 응용으로 유클리드 공간의 극소초평에서 L$^2$조화미분형식과 위상구조와의 관계를 살펴본다.
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Stress-energy tensor of the traceless Ricci tensor and Einstein-type manifolds
윤갑진 대한수학회 2024 대한수학회지 Vol.61 No.2
In this paper, we introduce the notion of stress-energy tensor $Q$ of the traceless Ricci tensor for Riemannian manifolds $(M^n, g)$, and investigate harmonicity of Riemannian curvature tensor and Weyl curvature tensor when $(M, g)$ satisfies some geometric structure such as critical point equation or vacuum static equation for smooth functions.
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On the structure of minimal submanifolds in a Riemannian manifold of non-negative curvature
윤갑진,김동호 대한수학회 2009 대한수학회보 Vol.46 No.6
Let M^{n} be a complete oriented non-compact minimally immersed submanifold in a complete Riemannian manifold N^{n+p} of non-negative curvature. We prove that if M is super-stable, then there are no non-trivial L^2 harmonic one forms on M. This is a generalization of the main result in [8]. Let M^{n} be a complete oriented non-compact minimally immersed submanifold in a complete Riemannian manifold N^{n+p} of non-negative curvature. We prove that if M is super-stable, then there are no non-trivial L^2 harmonic one forms on M. This is a generalization of the main result in [8].
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Schwarzschild 다양체 상에서 Green 함수의 움직임
윤갑진 명지대학교 자연과학연구소 2004 자연과학논문집 Vol.23 No.-
In this article, we compute the minimal Green function on the Schwarzschild manifold M = R^(2) X S^(2) and study its properties including the behavior at infinity 이 논문에서 우리는 Schwarzschild 리만계량을 갖는 다양체 M = R^(2) X S^(2)의 최소 Green 함수를 계산하고 이 함수의 무한대에서의 성질에 대하여 조사하였다.
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On the Behavior of Green's Function on the Schwarzschild Manifold
Yun, Gab-Jin 명지대학교 자연과학연구소 2004 자연과학논문집 Vol.23 No.-
이 논문에서 우리는 Schwarzschild 리만계량을 갖는 다양체 M = R^(2) X S^(2)의 최소 Green 함수를 계산하고 이 함수의 무한대에서의 성질에 대하여 조사하였다. In this article, we compute the minimal Green function on the Schwarzschild manifold M = R^(2) X S^(2) and study its properties including the behavior at infinity
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