• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.117-135
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• 2018

The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. Further, we obtain some results on these type of curves in ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$, respectively.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.121-134
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• 2022

In this study, we obtain the spherical images of minimal curves in the complex space in ℂ⁴ which are obtained by translating Cartan frame vector fields to the centre of hypersphere, and present their properties such as becoming isotropic cubic, pseudo helix, and spherical involutes. Also, we examine minimal curves which are characterized by a system of differential equations.

• Archives of Craniofacial Surgery
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• v.16 no.2
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• pp.92-95
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• 2015

A keratoacanthoma is a rapidly growing cutaneous tumor that spontaneously involutes in most instances. A giant keratoacanthoma is a rare variant and are characterized by lesions larger than 20 mm in diameter. We report a 56-year-old man with a rapidly growing tumor of the right cheek, which was diagnosed as keratoacanthoma. The mass was excised completely under general anesthesia, followed by Limberg flap for reconstruction. Intraoperative frozen section histology suggested the lesion to be a well-differentiated squamous cell carcinoma, whereas final histopathology was consistent with keratoacanthoma. We herein report the first case of a giant keratoacanthoma treated with surgical excision in Korea and discuss the clinical and histopathological features of keratoacanthoma, with a review of the literature.

• The Journal of Korean Orthopaedic Ultrasound Society
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• v.5 no.2
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• pp.99-101
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• 2012

Median artery of the forearm and wrist is not very frequently observed because it normally involutes before birth. Persistent median artery of the carpal tunnel is not frequently observed in adult life. We report a case of persistent median artery in the carpal tunnel that was examed by ultrasonography.

• Journal of Korean Foot and Ankle Society
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• v.19 no.1
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• pp.27-31
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• 2015

Intraosseous lipoma is a benign tumor that originates from proliferating mature lipocytes. It often occurs in the metaphysis of long bones of the lower extremity, and also in the calcaneus, humerus, mandible, sacrum, and rib bones. Frequently, it involutes spontaneously through a process of infarction, calcification, and cyst formation. It can either present as pain, or be asymptomatic and only discovered through an incidental radiological finding. In our case, the patient presented with heel pain. Intraoperatively, it was found that the intraosseous cavity was filled with fat along with an adjacent but separate area of cystic degeneration. There was also a cortical perforation at the cystic lesion which was communicating with the subtalar joint. This cortical breach is most likely the cause of diffuse lateral heel pain experienced by our patient, and such a pathological fracture due to intraosseous lipoma has never been reported.