Is it possible to create concave corners like this in css? If yes, how would you do it?

Lea Verou has a description of how to do this:
By using radial gradients, you can simulate rounded corners with a negative radius. You can do this without the support of any extra elements. Its a little tricky.
It also falls back to a solid color background if CSS gradients are not supported. It will work on Firefox 3.6, latest Webkit and —hopefully— Opera 11.10 (they announced that gradients support is coming). You could add a
-webkit-gradient()background too, to make it work in practically all versions of Webkit currently in use, but I warn you: It’s not going to be easy and I personally refuse to spend more than 5 minutes of my time messing with that non-standard thing.
Here is a live demo of their implementation.
Here is a good example of how I would tackle this:
HTML:
<div class='concave'>
<div class='topleftconcave'></div>
<div class='botleftconcave'></div>
</div>
CSS:
div.concave {
background:blue;
width:150px;
height:120px;
position:relative;
}
div.topleftconcave {
position:absolute;
background:white;
width:25px;
height:35px;
border-bottom-right-radius:500px;
}
div.botleftconcave {
position:absolute;
background:white;
width:25px;
height:35px;
bottom:0;
left:0;
border-top-right-radius:500px;
}
If you'd rather not add extra elements to the HTML, need to style only two corners and are able to use generated content instead, I'd suggest:
.concave {
position: relative;
width: 10em;
height: 3em;
line-height: 3em;
margin: 1em auto;
padding: 0.5em;
background-color: #00f;
color: #fff;
}
.concave::before {
content: '';
position: absolute;
top: -1em;
left: -1em;
border: 1em solid #fff;
border-radius: 1em;
}
.concave::after {
content: '';
position: absolute;
bottom: -1em;
left: -1em;
border: 1em solid #fff;
border-radius: 1em;
}
The only way I know is to add four divs at the four corners, each with a positive border radius.
What about the CSS3 border-image property? Great article here:
http://css-tricks.com/understanding-border-image/
It will mean no support for older browsers such as IE 7-8, but if you can live with that or find a work around this would work well.
I recently done used border-image myself to do this exact thing.