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Description
Convex SurfacesIn this self contained geometry text, the author describes the main results of convex surface theory, providing all definitions and precise theorems. The first half focuses on extrinsic geometry and applications of the Brunn Minkowski theory. The second part examines intrinsic geometry and the realization of intrinsic metrics. Starting with a brief overview of notations and terminology, the text proceeds to convex curves, the theorems of Meusnier and
In this self-contained geometry text, the author describes the main results of convex surface theory, providing all definitions and precise theorems. The first half focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. The second part examines intrinsic geometry and the realization of intrinsic metrics.Starting with a brief overview of notations and terminology, the text proceeds to convex curves, the theorems of Meusnier and Euler, extrinsic Gauss curvature, and the influence of the curvature on the local shape of a surface. A chapter on the Brunn-Minkowski theory and its applications is followed by examinations of intrinsic metrics, the metrics of convex hypersurfaces, geodesics, angles, triangulations, and the Gauss-Bonnet theorem. The final chapter explores the rigidity of convex polyhedra, the realization of polyhedral metrics, Weyl's problem, local realization of metrics with non-negative curvature, open and closed surfaces, and smoothness of realizations.
Binding Type: Paperback
Publisher: Dover Publications
Published: 02/04/2008
ISBN: 9780486462431
Pages: 196
Weight: 0.47lbs
Size: 8.44h x 5.88w x 0.43d
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4.3 ★★★★★
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★★★★★ 3
They definitely whiten, but caused severe sensitivity
I have mixed feelings about these whitening strips. On the positive side, they absolutely do what they promise, my teeth are noticeably whiter, and the actual whitening results were fantastic.
However, they left my teeth painfully sensitive. I was very careful to follow the instructions exactly and made sure I only left them on for the strictly recommended amount of time, but I still experienced intense, lingering sensitivity afterward.
If you have a high tolerance or don't usually struggle with sensitive teeth, these might be a great fit for you since they really do work. But if you are prone to sensitivity at all, I would definitely proceed with caution!
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Reviewed in the United States on May 22, 2026
★★★★★ 5
Good product good price
The best white strips I’ve ever tried quick and easy note we taste afterwards
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Reviewed in the United States on June 3, 2026
★★★★★ 5
Gorgeous wig, big head friendly
Color: 1B Off Black
I loved this wig, I have a huge head and have to return now wigs I buy.
But this was a keeper, it's synthetic so don't go crazy expecting human hair realness.
In the sense that it will tangle in the nape.
I detailed and then cut off the undesirables.
But for the prize, it worked as half wig with a headband.
For the price you can't beat it.
I gelled the front alittle and I looked like Selena. Lol if you know the reference then you know.
But it looked great with a headband.
I wore it on vacation it wasn't too hot, it wasn't exactly cool either.
But it was good.
For the price I'm buying a few more in other colors.
I didn't make it a ponytail yet but that up next.
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Reviewed in the United States on June 12, 2023
★★★★★ 3
Good quality
Color: 1B Off Black
Good quality. Covers whole head
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Reviewed in the United States on July 8, 2025
★★★★★ 4
Decent for the price
Color: 2 Dark Brown, Color: 2 Dark Brown
Bought the color 2 thinking it would be brown but it’s almost Black (my own ignorance). I saw a YT vid by Kie Rashon where she sort of left the front of her hair out so I was hoping to do the same but it’s too dark for my hair (you can’t tell in the pics). I would recommend checking Kie out on YT for more details.
I do like it though so I will probably give this one to my sister and reorder a different color. Wish they provided pics of how the wig in other colors look.
Edit: So I repurchased this piece in DR Hazelnut Brown (the lighter color). I took some leave out in the front so please note that’s my hairline, not the wig’s. It blended well with my hair color. My texture is a little curlier but I just did a braid out on the front to help it blend. Wig tangles very easily. I’m going to experiment with co-washing to see if that reverts it to its origami condition.
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Reviewed in the United States on December 7, 2022